waveslim/0000755000176000001440000000000013622230602012125 5ustar ripleyuserswaveslim/NAMESPACE0000644000176000001440000000062113423100136013340 0ustar ripleyusersuseDynLib("waveslim") exportPattern("^[^\\.]") importFrom("grDevices", "rainbow") importFrom("graphics", "axis", "box", "image", "lines", "mtext", "par", "plot") importFrom("stats", "convolve", "fft", "filter", "integrate", "lsfit", "mad", "median", "mvfft", "optim", "optimize", "pchisq", "qchisq", "qnorm", "rnorm", "runif", "spec.taper") S3method(plot, dwt.2d) waveslim/LICENSE0000644000176000001440000000013012453631330013130 0ustar ripleyusersYEAR: 1997-2013 COPYRIGHT HOLDER: Brandon Whitcher ORGANIZATION: Rigorous Analytics Ltd.waveslim/data/0000755000176000001440000000000012454055721013047 5ustar ripleyuserswaveslim/data/datalist0000644000176000001440000000025112454055716014601 0ustar ripleyusersacvs.andel10 acvs.andel11 acvs.andel8 acvs.andel9 ar1 barbara blocks cpi dau doppler exchange heavisine ibm japan jumpsine kobe linchirp mexm nile tourism unemploy xbox waveslim/data/tourism.rda0000644000176000001440000000113213423103656015234 0ustar ripleyusersmKSqD!DtFuTt./ ev-Q̽QΗʎfeRbSL2aS)nmNDĺ)< :0?{^{XCBIȹdM27ӯ;Zrʥ S X? x UZw*Zsּ9hש}j%oއ\WcnMb~4r-]un3x?sYkݬ'Yz&vÌ-u$%Nt}WYD\zj]6sGї%"wnGYTg +=Zv!HnUM3JJz6;tQRwaveslim/data/acvs.andel10.rda0000644000176000001440000014026413423103655015722 0ustar ripleyusers7zXZi"6!X@u])TW"nRʟ"d[:!';i^uѡ9HwgU?ß]A䅲]}srńf@5D:z~{DGG=L&J FS3%Kפ},;HS|Gk[57^\h@Rn^0AV~OɖCb2k5D}!Ţ-Ƌ7[kJZǴ%Kj/SHg24<(D K ~)vPE0x b4;UJD7n&tᓟ.C+=*JIϒ+^u=anqېVñXޯ)Rjܗ1a(2Ciuڍȝf#9E %V;ps3)#pLW5wg?\(Eوkˊ)n~h$rpЄO\NAY1)Զi!)3Y-#]nhMF:-\s:ЏZ e)(J rY%Los{)ikyoB>XdOfNh% ݦZh輭/[TI;>"6lud52* 9^k~r_8II#r֎OfbfbN )ZnL<|O }R6)"NO!%׽]4!$6G@ 8<: sBp}nC3櫔KtDu<5)3x HU K&+QcX㵘K=&nM>/pf U<#߱fe<'x1l/i CD>4,Aۖ/52rV_I+NTe\j4_=MAdp4ˤhw̸(ZO Jys\{۝ǣ,tu,@GNٹ/tȅ)kEJ>9<(nH[{eVީ4Pp ȑ4[(v;CܶB49Cz->)ق &^MB+p;ᗈ>c:-!7dڨ7#pҋe(hY>@Ɋ5u[QЮPG X֡R8wdvVg[78t˔Cbb eQ?_OO:ھ|m37"厜g_p䚩l?o')^eƇM؏y|>ih@m(_ErQHrˮI--q )a ^dEa';-U*==)[W?Le}IeD@$L,vc<o`iƇs"l$W{xb tݘfX/չ5/l2RfN&'|abi Gn/yBEWី;P0Hp|W$VonXK%lHJ]vm g>21FH~}{h0ie%/N5kT{cSF6'{[A܆1CXD)vn5yqß /JW7=zRwΫVK?Awgy:EKaaUرz|T\i|yb/؀I-eFT EA6uYF`a++!<,7{ͧB jN&3(EИ,E&A;Ǚ䑈v&~S 9ܫ- [ӢN QpLDT2;9tg}Zr>.u!Y|\Ss DsDʶd'4ݥ|0_R2T LXpd%kw*H`'UD~^1+9NH9HUru"W,҄ j;_=icؿ ӗl5Px=i*?|9!R:>usΥoԜ ð ]ykj34SY&UzqnU hT<8ێB4F iu{ܸʗȀdcSq{e=l7F iGCpeM=ܘเc71U\#c2‰15f,덋,di9]F;08Ts NͼS*/k \va"1Ú ;JMuG% 9G慫yu> A"qunMGEFH=X&8=2O vi G*{o18ԀMna?Kvv1 [mZv]We|MLn2<(&Z>YrEnE}m8O K xJG2%ׯ4/K4V,S>#gjTs 7k/Y|7U2~yEؠ,9e np y1)rn_Ä԰9]\\ V1Q.ˀpbt~R>Iad%G.z}b'lZ4Gn!>W5mf]ܶJ%,Ĭ Lػ;(4A*-a'Sv\>* YYй})#ݻ?=̲ܺ/}-<,ξON;r޿Rai1.+*eI,ߏRȐ?l:~mJ kuSx,QiXK>j) tmX% 1ju%8:^$D=pJ-5ۏ 67$J&EUKXyMH'-vvYm^ӣM$$^f5$-5%hmb5b JпE?=Ś$qj{%;`>(Vr(mŨ|+.gN'Y_iVJ criz~l6T?XN5 ]㫉Jnpכ:d5 OY˴^i uŝY@6E:t#0e4%9ܼagV$> ~2.a#)@Zy봣w$W_ؕ`I8TH[/_?)8׻Il|})Ie/wfcLh@:n(`L#f."v^^:#M9_Æ}O0ɀ!kEuG,EI=6P YIHP^j+|a=x~DY5nLa`JHJ~KB7kcC5x |[XxgUWx=@ h*Q"ݖ z [,g!FymT]~#x(m&?ɮ}p)Dlm.Q>%~̆oP76O}z1n@X}.Yugfg_EmsXz%Xxd$ʟdxjg REG; KL*uhd6mZFXb"z?,G9.=x3 Fщ- {`'FrǤ<'5,3'MhwHkj!xr\K: +6f ?czLdlxjg_GW[tљrZ2SӤσlhL1!sV'xoc{dGq̔LU;#$cƠJ^8tnמ5"Z{pm3]כ%V!4u5S 쓃 5 ,eWDt&)uwiMIЎ+F#vA Fk LK/b Vf4jAHj)Zk۳^Lt>E=kiϑ f$ņm0OHl9کfOo8CS֒3m ^! f{NS=TjahɦϧiIDVx6şQ$ܦ\$e-.A6lFuvDvP%727.l (,nV̔6I''Cڒ4_663g.ZYIK4rJMhq Oqy[Az6%Ts_`+h+|i)|!~" xYj9TzbŽohAg9y!Wi6=ޫ7--s,^ZoS _PoB\!s!@6+hma†|*Xzf F8ڠ,Nȸ€S޿(SAB]9P`6;(ϔS#Иv]CU1C (uOM|x% xWKq־0EkLjQ)j;kefGki+n4?rh?ΔPv>k(Y+cE/ƒ24;$`Osr.e/! 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UN$}{\code{M} > \code{N}} a uniform random variable is generated in order to select a random piece of the simulated time series. For more details see Whitcher (2001). } \references{ Hosking, J. R. M. (1981) Fractional Differencing, \emph{Biometrika}, \bold{68}, No. 1, 165-176. Whitcher, B. (2001) Simulating Gaussian Stationary Time Series with Unbounded Spectra, \emph{Journal of Computational and Graphical Statistics}, \bold{10}, No. 1, 112-134. } \seealso{ \code{\link{hosking.sim}} for an exact time-domain method and \code{\link{wave.filter}} for a list of available wavelet filters. } \examples{ ## Generate monthly time series with annual oscillation ## library(ts) is required in order to access acf() x <- dwpt.sim(256, "mb16", .4, 1/12, M=4, epsilon=.001) par(mfrow=c(2,1)) plot(x, type="l", xlab="Time") acf(x, lag.max=128, ylim=c(-.6,1)) data(acvs.andel8) lines(acvs.andel8$lag[1:128], acvs.andel8$acf[1:128], col=2) } \author{B. Whitcher} \keyword{ts} waveslim/man/convolve2D.Rd0000644000176000001440000000240612453631333015221 0ustar ripleyusers\name{convolve2D} \alias{convolve2D} \title{Fast Column-wise Convolution of a Matrix} \description{ Use the Fast Fourier Transform to perform convolutions between a sequence and each column of a matrix. } \usage{ convolve2D(x, y, conj = TRUE, type = c("circular", "open")) } \arguments{ \item{x}{\eqn{M{\times}N} matrix.} \item{y}{numeric sequence of length \eqn{N}.} \item{conj}{logical; if \code{TRUE}, take the complex \emph{conjugate} before back-transforming (default, and used for usual convolution).} \item{type}{character; one of \code{circular}, \code{open} (beginning of word is ok). For \code{circular}, the two sequences are treated as \emph{circular}, i.e., periodic. For \code{open} and \code{filter}, the sequences are padded with zeros (from left and right) first; \code{filter} returns the middle sub-vector of \code{open}, namely, the result of running a weighted mean of \code{x} with weights \code{y}.} } %\value{} \details{ This is a corrupted version of \code{convolve} made by replacing \code{fft} with \code{mvfft} in a few places. It would be nice to submit this to the R Developers for inclusion. } %\references{} \seealso{ \code{\link{convolve}} } %\examples{} \author{Brandon Whitcher} \keyword{ts} waveslim/man/fdp.mle.Rd0000644000176000001440000000467212453631333014534 0ustar ripleyusers\name{fdp.mle} \alias{fdp.mle} \title{Wavelet-based Maximum Likelihood Estimation for a Fractional Difference Process} \description{ Parameter estimation for a fractional difference (long-memory, self-similar) process is performed via maximum likelihood on the wavelet coefficients. } \usage{fdp.mle(y, wf, J=log(length(y),2)) } \arguments{ \item{y}{Dyadic length time series.} \item{wf}{Name of the wavelet filter to use in the decomposition. See \code{\link{wave.filter}} for those wavelet filters available.} \item{J}{Depth of the discrete wavelet transform.} } \value{ List containing the maximum likelihood estimates (MLEs) of \eqn{d} and \eqn{\sigma^2}, along with the value of the likelihood for those estimates. } \details{ The variance-covariance matrix of the original time series is approximated by its wavelet-based equivalent. A Whittle-type likelihood is then constructed where the sums of squared wavelet coefficients are compared to bandpass filtered version of the true spectrum. Minimization occurs only for the fractional difference parameter \eqn{d}, while variance is estimated afterwards. } \references{ M. J. Jensen (2000) An alternative maximum likelihood estimator of long-memory processes using compactly supported wavelets, \emph{Journal of Economic Dynamics and Control}, \bold{24}, No. 3, 361-387. McCoy, E. J., and A. T. Walden (1996) Wavelet analysis and synthesis of stationary long-memory processes, \emph{Journal for Computational and Graphical Statistics}, \bold{5}, No. 1, 26-56. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } %\seealso{} \examples{ ## Figure 5.5 in Gencay, Selcuk and Whitcher (2001) fdp.sdf <- function(freq, d, sigma2=1) sigma2 / ((2*sin(pi * freq))^2)^d dB <- function(x) 10 * log10(x) per <- function(z) { n <- length(z) (Mod(fft(z))**2/(2*pi*n))[1:(n \%/\% 2 + 1)] } data(ibm) ibm.returns <- diff(log(ibm)) ibm.volatility <- abs(ibm.returns) ibm.vol.mle <- fdp.mle(ibm.volatility, "d4", 4) freq <- 0:184/368 ibm.vol.per <- 2 * pi * per(ibm.volatility) ibm.vol.resid <- ibm.vol.per/ fdp.sdf(freq, ibm.vol.mle$parameters[1]) par(mfrow=c(1,1), las=0, pty="m") plot(freq, dB(ibm.vol.per), type="l", xlab="Frequency", ylab="Spectrum") lines(freq, dB(fdp.sdf(freq, ibm.vol.mle$parameters[1], ibm.vol.mle$parameters[2]/2)), col=2) } \author{B. Whitcher} \keyword{ts} waveslim/man/hwt.analysis.Rd0000644000176000001440000000345012453631333015624 0ustar ripleyusers\name{HWP Analysis} \alias{modhwt.coh} \alias{modhwt.phase} \alias{modhwt.coh.seasonal} \alias{modhwt.phase.seasonal} \title{Time-varying and Seasonal Analysis Using Hilbert Wavelet Pairs} \description{ Performs time-varying or seasonal coherence and phase anlaysis between two time seris using the maximal-overlap discrete Hilbert wavelet transform (MODHWT). } \usage{ modhwt.coh(x, y, f.length = 0) modhwt.phase(x, y, f.length = 0) modhwt.coh.seasonal(x, y, S = 10, season = 365) modhwt.phase.seasonal(x, y, season = 365) } \arguments{ \item{x}{MODHWT object.} \item{y}{MODHWT object.} \item{f.length}{Length of the rectangular filter.} \item{S}{Number of "seasons".} \item{season}{Length of the "season".} } \value{ Time-varying or seasonal coherence and phase between two time series. The coherence estimates are between zero and one, while the phase estimates are between \eqn{-\pi}{-pi} and \eqn{\pi}{pi}. } \details{ The idea of seasonally-varying spectral analysis (SVSA, Madden 1986) is generalized using the MODWT and Hilbert wavelet pairs. For the seasonal case, \eqn{S} seasons are used to produce a consistent estimate of the coherence and phase. For the non-seasonal case, a simple rectangular (moving-average) filter is applied to the MODHWT coefficients in order to produce consistent estimates. } \references{ Madden, R.A. (1986). Seasonal variation of the 40--50 day oscillation in the tropics. \emph{Journal of the Atmospheric Sciences\/} \bold{43\/}(24), 3138--3158. Whither, B. and P.F. Craigmile (2004). Multivariate Spectral Analysis Using Hilbert Wavelet Pairs, \emph{International Journal of Wavelets, Multiresolution and Information Processing}, to appear. } \seealso{ \code{\link{hilbert.filter}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/basis.Rd0000644000176000001440000000216312453631333014301 0ustar ripleyusers\name{basis} \alias{basis} \title{Produce Boolean Vector from Wavelet Basis Names} \description{ Produce a vector of zeros and ones from a vector of basis names. } \usage{basis(x, basis.names) } \arguments{ \item{x}{Output from the discrete wavelet package transfrom (DWPT).} \item{basis.names}{Vector of character strings that describe leaves on the DWPT basis tree. See the examples below for appropriate syntax.} } \value{ Vector of zeros and ones. } \details{ None. } %\references{} \seealso{ \code{\link{dwpt}}. } \examples{ data(acvs.andel8) \dontrun{ x <- hosking.sim(1024, acvs.andel8[,2]) x.dwpt <- dwpt(x, "la8", 7) ## Select orthonormal basis from wavelet packet tree x.basis <- basis(x.dwpt, c("w1.1","w2.1","w3.0","w4.3","w5.4","w6.10", "w7.22","w7.23")) for(i in 1:length(x.dwpt)) x.dwpt[[i]] <- x.basis[i] * x.dwpt[[i]] ## Resonstruct original series using selected orthonormal basis y <- idwpt(x.dwpt, x.basis) par(mfrow=c(2,1), mar=c(5-1,4,4-1,2)) plot.ts(x, xlab="", ylab="", main="Original Series") plot.ts(y, xlab="", ylab="", main="Reconstructed Series") } } \keyword{ts} waveslim/man/sdf.Rd0000644000176000001440000000312712453631333013755 0ustar ripleyusers\name{Spectral Density Functions} \alias{fdp.sdf} \alias{spp.sdf} \alias{spp2.sdf} \alias{sfd.sdf} \title{Spectral Density Functions for Long-Memory Processes} \description{ Draws the spectral density functions (SDFs) for standard long-memory processes including fractional difference (FD), seasonal persistent (SP), and seasonal fractional difference (SFD) processes. } \usage{fdp.sdf(freq, d, sigma2 = 1) spp.sdf(freq, d, fG, sigma2 = 1) spp2.sdf(freq, d1, f1, d2, f2, sigma2 = 1) sfd.sdf(freq, s, d, sigma2 = 1) } \arguments{ \item{freq}{vector of frequencies, normally from 0 to 0.5} \item{d,d1,d2}{fractional difference parameter} \item{fG,f1,f2}{Gegenbauer frequency} \item{s}{seasonal parameter} \item{sigma2}{innovations variance} } \value{ The power spectrum from an FD, SP or SFD process. } %\details{} %\references{} \seealso{ \code{\link{fdp.mle}}, \code{\link{spp.mle}}. } \examples{ dB <- function(x) 10 * log10(x) fdp.main <- expression(paste("FD", group("(",d==0.4,")"))) sfd.main <- expression(paste("SFD", group("(",list(s==12, d==0.4),")"))) spp.main <- expression(paste("SPP", group("(",list(delta==0.4, f[G]==1/12),")"))) freq <- 0:512/1024 par(mfrow=c(2,2), mar=c(5-1,4,4-1,2), col.main="darkred") plot(freq, dB(fdp.sdf(freq, .4)), type="l", xlab="frequency", ylab="spectrum (dB)", main=fdp.main) plot(freq, dB(spp.sdf(freq, .4, 1/12)), type="l", xlab="frequency", ylab="spectrum (dB)", font.main=1, main=spp.main) plot(freq, dB(sfd.sdf(freq, 12, .4)), type="l", xlab="frequency", ylab="spectrum (dB)", main=sfd.main) } \author{Brandon Whitcher} \keyword{ts} waveslim/man/dwt.3d.Rd0000644000176000001440000000126512453631333014305 0ustar ripleyusers\name{dwt.3d} \alias{dwt.3d} \alias{idwt.3d} \title{Three Dimensional Separable Discrete Wavelet Transform} \description{ Three-dimensional separable discrete wavelet transform (DWT). } \usage{ dwt.3d(x, wf, J=4, boundary="periodic") idwt.3d(y) } \arguments{ \item{x}{input array} \item{wf}{name of the wavelet filter to use in the decomposition} \item{J}{depth of the decomposition, must be a number less than or equal to \eqn{\log_2(\min\{X,Y,Z\})}{log(min{Z,Y,Z},2)}} \item{boundary}{only \code{"periodic"} is currently implemented} \item{y}{an object of class \code{dwt.3d}} } %\value{} %\details{} %\references{} %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/my.acf.Rd0000644000176000001440000000157512453631333014363 0ustar ripleyusers\name{my.acf} \alias{my.acf} \alias{my.ccf} \title{Autocovariance Functions via the Discrete Fourier Transform} \description{ Computes the autocovariance function (ACF) for a time series or the cross-covariance function (CCF) between two time series. } \usage{my.acf(x) my.ccf(a, b) } \arguments{ \item{x,a,b}{time series} } \value{ The autocovariance function for all nonnegative lags or the cross-covariance function for all lags. } \details{ The series is zero padded to twice its length before the discrete Fourier transform is applied. Only the values corresponding to nonnegative lags are provided (for the ACF). } %\references{} %\seealso{} \examples{ data(ibm) ibm.returns <- diff(log(ibm)) plot(1:length(ibm.returns) - 1, my.acf(ibm.returns), type="h", xlab="lag", ylab="ACVS", main="Autocovariance Sequence for IBM Returns") } \author{B. Whitcher} \keyword{ts} waveslim/man/ibm.Rd0000644000176000001440000000070412453631333013746 0ustar ripleyusers\name{ibm} \alias{ibm} \title{Daily IBM Stock Prices} \description{ Daily IBM stock prices spanning May~17, 1961 to November~2, 1962. } \usage{data(ibm) } \format{A vector containing 369 observations. } \source{ Box, G. E.~P. and Jenkins, G.~M. (1976) \emph{Time Series Analysis: Forecasting and Control}, Holden Day, San Francisco, 2 edition. } \references{ \url{http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/} } \keyword{datasets} waveslim/man/dwt.2d.Rd0000644000176000001440000000321412453631333014300 0ustar ripleyusers\name{dwt.2d} \alias{dwt.2d} \alias{idwt.2d} \title{Two-Dimensional Discrete Wavelet Transform} \description{ Performs a separable two-dimensional discrete wavelet transform (DWT) on a matrix of dyadic dimensions. } \usage{dwt.2d(x, wf, J = 4, boundary = "periodic") idwt.2d(y) } \arguments{ \item{x}{input matrix (image)} \item{wf}{name of the wavelet filter to use in the decomposition} \item{J}{depth of the decomposition, must be a number less than or equal to \eqn{\log_2(\min\{M,N\})}{log(min{M,N},2)}} \item{boundary}{only \code{"periodic"} is currently implemented} \item{y}{an object of class \code{dwt.2d}} } \value{ List structure containing the \eqn{3J+1} sub-matrices from the decomposition. } \details{ See references. } \references{ Mallat, S. (1998) \emph{A Wavelet Tour of Signal Processing}, Academic Press. Vetterli, M. and J. Kovacevic (1995) \emph{Wavelets and Subband Coding}, Prentice Hall. } \seealso{ \code{\link{modwt.2d}}. } \examples{ ## Xbox image data(xbox) xbox.dwt <- dwt.2d(xbox, "haar", 3) par(mfrow=c(1,1), pty="s") plot.dwt.2d(xbox.dwt) par(mfrow=c(2,2), pty="s") image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox, xlab="", ylab="", main="Original Image") image(1:dim(xbox)[1], 1:dim(xbox)[2], idwt.2d(xbox.dwt), xlab="", ylab="", main="Wavelet Reconstruction") image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox - idwt.2d(xbox.dwt), xlab="", ylab="", main="Difference") ## Daubechies image data(dau) par(mfrow=c(1,1), pty="s") image(dau, col=rainbow(128)) sum(dau^2) dau.dwt <- dwt.2d(dau, "d4", 3) plot.dwt.2d(dau.dwt) sum(plot.dwt.2d(dau.dwt, plot=FALSE)^2) } \author{B. Whitcher} \keyword{ts} waveslim/man/ar1.Rd0000644000176000001440000000063312453631333013663 0ustar ripleyusers\name{ar1} \alias{ar1} \title{Simulated AR(1) Series} \description{ Simulated AR(1) series used in Gencay, Selcuk and Whitcher (2001). } \usage{data(ar1) } \format{A vector containing 200 observations. } %\source{} \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/modwt.2d.Rd0000644000176000001440000000506012453631333014635 0ustar ripleyusers\name{modwt.2d} \alias{modwt.2d} \alias{imodwt.2d} \title{Two-Dimensional Maximal Overlap Discrete Wavelet Transform} \description{ Performs a separable two-dimensional maximal overlap discrete wavelet transform (MODWT) on a matrix of arbitrary dimensions. } \usage{modwt.2d(x, wf, J = 4, boundary = "periodic") imodwt.2d(y) } \arguments{ \item{x}{input matrix} \item{wf}{name of the wavelet filter to use in the decomposition} \item{J}{depth of the decomposition} \item{boundary}{only \code{"periodic"} is currently implemented} \item{y}{an object of class \code{dwt.2d}} } \value{ List structure containing the \eqn{3J+1} sub-matrices from the decomposition. } \details{ See references. } \references{ Liang, J. and T. W. Parks (1994) A two-dimensional translation invariant wavelet representation and its applications, \emph{Proceedings ICIP-94}, Vol. 1, 66-70. Liang, J. and T. W. Parks (1994) Image coding using translation invariant wavelet transforms with symmetric extensions, \emph{IEEE Transactions on Image Processing}, \bold{7}, No. 5, 762-769. } \seealso{ \code{\link{dwt.2d}}, \code{\link{shift.2d}}. } \examples{ ## Xbox image data(xbox) xbox.modwt <- modwt.2d(xbox, "haar", 2) ## Level 1 decomposition par(mfrow=c(2,2), pty="s") image(xbox.modwt$LH1, col=rainbow(128), axes=FALSE, main="LH1") image(xbox.modwt$HH1, col=rainbow(128), axes=FALSE, main="HH1") frame() image(xbox.modwt$HL1, col=rainbow(128), axes=FALSE, main="HL1") ## Level 2 decomposition par(mfrow=c(2,2), pty="s") image(xbox.modwt$LH2, col=rainbow(128), axes=FALSE, main="LH2") image(xbox.modwt$HH2, col=rainbow(128), axes=FALSE, main="HH2") image(xbox.modwt$LL2, col=rainbow(128), axes=FALSE, main="LL2") image(xbox.modwt$HL2, col=rainbow(128), axes=FALSE, main="HL2") sum((xbox - imodwt.2d(xbox.modwt))^2) data(dau) par(mfrow=c(1,1), pty="s") image(dau, col=rainbow(128), axes=FALSE, main="Ingrid Daubechies") sum(dau^2) dau.modwt <- modwt.2d(dau, "d4", 2) ## Level 1 decomposition par(mfrow=c(2,2), pty="s") image(dau.modwt$LH1, col=rainbow(128), axes=FALSE, main="LH1") image(dau.modwt$HH1, col=rainbow(128), axes=FALSE, main="HH1") frame() image(dau.modwt$HL1, col=rainbow(128), axes=FALSE, main="HL1") ## Level 2 decomposition par(mfrow=c(2,2), pty="s") image(dau.modwt$LH2, col=rainbow(128), axes=FALSE, main="LH2") image(dau.modwt$HH2, col=rainbow(128), axes=FALSE, main="HH2") image(dau.modwt$LL2, col=rainbow(128), axes=FALSE, main="LL2") image(dau.modwt$HL2, col=rainbow(128), axes=FALSE, main="HL2") sum((dau - imodwt.2d(dau.modwt))^2) } \author{B. Whitcher} \keyword{ts} waveslim/man/tourism.Rd0000644000176000001440000000063012453631333014677 0ustar ripleyusers\name{tourism} \alias{tourism} \title{U.S. Tourism} \description{ Quarterly U.S. tourism figures from 1960:1 to 1999:4. } \usage{data(tourism) } \format{A vector containing 160 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/modwt.Rd0000644000176000001440000000737012453631333014337 0ustar ripleyusers\name{modwt} \alias{modwt} \alias{imodwt} \title{(Inverse) Maximal Overlap Discrete Wavelet Transform} \description{ This function performs a level \eqn{J} decomposition of the input vector using the non-decimated discrete wavelet transform. The inverse transform performs the reconstruction of a vector or time series from its maximal overlap discrete wavelet transform. } \usage{modwt(x, wf = "la8", n.levels = 4, boundary = "periodic") imodwt(y) } \arguments{ \item{x}{ a vector or time series containing the data be to decomposed. There is \bold{no} restriction on its length. } \item{y}{ Object of class \code{"modwt"}. } \item{wf}{ Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} (Daubechies, 1992), least asymmetric family. } \item{n.levels}{ Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log_2(\mbox{length}(x))}{log(length(x),2)}. } \item{boundary}{ Character string specifying the boundary condition. If \code{boundary=="periodic"} the defaulTRUE, then the vector you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the vector beyond its boundaries is assumed to be a symmetric reflection of itself. } } \value{ Object of class \code{"modwt"}, basically, a list with the following components \item{d?}{Wavelet coefficient vectors.} \item{s?}{Scaling coefficient vector.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ The code implements the one-dimensional non-decimated DWT using the pyramid algorithm. The actual transform is performed in C using pseudocode from Percival and Walden (2001). That means convolutions, not inner products, are used to apply the wavelet filters. The MODWT goes by several names in the statistical and engineering literature, such as, the ``stationary DWT'', ``translation-invariant DWT'', and ``time-invariant DWT''. The inverse MODWT implements the one-dimensional inverse transform using the pyramid algorithm (Mallat, 1989). } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Percival, D. B. and P. Guttorp (1994) Long-memory processes, the Allan variance and wavelets, In \emph{Wavelets and Geophysics}, pages 325-344, Academic Press. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } \seealso{ \code{\link{dwt}}, \code{\link{idwt}}, \code{\link{mra}}. } \examples{ ## Figure 4.23 in Gencay, Selcuk and Whitcher (2001) data(ibm) ibm.returns <- diff(log(ibm)) # Haar ibmr.haar <- modwt(ibm.returns, "haar") names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4") # LA(8) ibmr.la8 <- modwt(ibm.returns, "la8") names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4") # shift the MODWT vectors ibmr.la8 <- phase.shift(ibmr.la8, "la8") ## plot partial MODWT for IBM data par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)") for(i in 1:5) plot.ts(ibmr.haar[[i]], axes=FALSE, ylab=names(ibmr.haar)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)") for(i in 1:5) plot.ts(ibmr.la8[[i]], axes=FALSE, ylab=names(ibmr.la8)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) } \author{B. Whitcher} \keyword{ts} waveslim/man/qmf.Rd0000644000176000001440000000121012453631333013753 0ustar ripleyusers\name{qmf} \alias{qmf} \title{Quadrature Mirror Filter} \description{ Computes the quadrature mirror filter from a given filter. } \usage{qmf(g, low2high=TRUE) } \arguments{ \item{g}{Filter coefficients.} \item{low2high}{Logical, default is \code{TRUE} which means a low-pass filter is input and a high-pass filter is output. Setting \code{low2high=F} performs the inverse.} } \value{ Quadrature mirror filter. } \details{ None. } \references{ Any basic signal processing text. } \seealso{ \code{\link{wave.filter}}. } \examples{ ## Haar wavelet filter g <- wave.filter("haar")$lpf qmf(g) } \author{B. Whitcher} \keyword{ts} waveslim/man/mra.2d.Rd0000644000176000001440000000554212453631333014267 0ustar ripleyusers\name{mra.2d} \alias{mra.2d} \title{Multiresolution Analysis of an Image} \description{ This function performs a level \eqn{J} additive decomposition of the input matrix or image using the pyramid algorithm (Mallat 1989). } \usage{mra.2d(x, wf = "la8", J = 4, method = "modwt", boundary = "periodic") } \arguments{ \item{x}{A matrix or image containing the data be to decomposed. This must be have dyadic length in both dimensions (but not necessarily the same) for \code{method="dwt"}.} \item{wf}{Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} least asymmetric family.} \item{J}{Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}{log(length(x),2)}.} \item{method}{Either \code{"dwt"} or \code{"modwt"}.} \item{boundary}{Character string specifying the boundary condition. If \code{boundary=="periodic"} the default, then the matrix you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the matrix beyond its boundaries is assumed to be a symmetric reflection of itself.} } \value{ Basically, a list with the following components \item{LH?}{Wavelet detail image in the horizontal direction.} \item{HL?}{Wavelet detail image in the vertical direction.} \item{HH?}{Wavelet detail image in the diagonal direction.} \item{LL\eqn{J}}{Wavelet smooth image at the coarsest resolution.} \item{\eqn{J}}{Depth of the wavelet transform.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ This code implements a two-dimensional multiresolution analysis by performing the one-dimensional pyramid algorithm (Mallat 1989) on the rows and columns of the input matrix. Either the DWT or MODWT may be used to compute the multiresolution analysis, which is an additive decomposition of the original matrix (image). } \references{ Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Mallat, S. G. (1998) \emph{A Wavelet Tour of Signal Processing}, Academic Press. } \seealso{ \code{\link{dwt.2d}}, \code{\link{modwt.2d}} } \author{B. Whitcher} \examples{ ## Easy check to see if it works... ## -------------------------------- x <- matrix(rnorm(32*32), 32, 32) # MODWT x.mra <- mra.2d(x, method="modwt") x.mra.sum <- x.mra[[1]] for(j in 2:length(x.mra)) x.mra.sum <- x.mra.sum + x.mra[[j]] sum((x - x.mra.sum)^2) # DWT x.mra <- mra.2d(x, method="dwt") x.mra.sum <- x.mra[[1]] for(j in 2:length(x.mra)) x.mra.sum <- x.mra.sum + x.mra[[j]] sum((x - x.mra.sum)^2) } \keyword{ts} waveslim/man/ortho.basis.Rd0000644000176000001440000000237612453631333015441 0ustar ripleyusers\name{ortho.basis} \alias{ortho.basis} \title{Derive Orthonormal Basis from Wavelet Packet Tree} \description{ An orthonormal basis for the discrete wavelet transform may be characterized via a disjoint partitioning of the frequency axis that covers \eqn{[0,\frac{1}{2})}{[0,1/2)}. This subroutine produces an orthonormal basis from a full wavelet packet tree. } \usage{ortho.basis(xtree) } \arguments{ \item{xtree}{is a vector whose entries are associated with a wavelet packet tree.} } \value{ Boolean vector describing the orthonormal basis for the DWPT. } \details{ A wavelet packet tree is a binary tree of Boolean variables. Parent nodes are removed if any of their children exist. } %\references{} %\seealso{} \examples{ data(japan) J <- 4 wf <- "mb8" japan.mra <- mra(log(japan), wf, J, boundary="reflection") japan.nomean <- ts(apply(matrix(unlist(japan.mra[-(J+1)]), ncol=J, byrow=FALSE), 1, sum), start=1955, freq=4) japan.nomean2 <- ts(japan.nomean[42:169], start=1965.25, freq=4) plot(japan.nomean2, type="l") japan.dwpt <- dwpt(japan.nomean2, wf, 6) japan.basis <- ortho.basis(portmanteau.test(japan.dwpt, p=0.01, type="other")) # Not implemented yet # par(mfrow=c(1,1)) # plot.basis(japan.basis) } \author{B. Whitcher} \keyword{ts} waveslim/man/Andel.Rd0000644000176000001440000000140512453631333014221 0ustar ripleyusers\name{Andel} \alias{acvs.andel8} \alias{acvs.andel9} \alias{acvs.andel10} \alias{acvs.andel11} \title{Autocovariance and Autocorrelation Sequences for a Seasonal Persistent Process} \description{ The autocovariance and autocorrelation sequences from the time series model in Figures 8, 9, 10, and 11 of Andel (1986). They were obtained through numeric integration of the spectral density function. } \usage{data(acvs.andel8) data(acvs.andel9) data(acvs.andel10) data(acvs.andel11) } \format{ A data frame with 4096 rows and three columns: lag, autocovariance sequence, autocorrelation sequence. } \references{ Andel, J. (1986) Long memory time series models, \emph{Kypernetika}, \bold{22}, No. 2, 105-123. } \keyword{datasets} waveslim/man/hilbert.filter.Rd0000644000176000001440000000243412453631333016116 0ustar ripleyusers\name{hilbert.filter} \alias{hilbert.filter} \title{Select a Hilbert Wavelet Pair} \description{ Converts name of Hilbert wavelet pair to filter coefficients. } \usage{ hilbert.filter(name) } \arguments{ \item{name}{Character string of Hilbert wavelet pair, see acceptable names below (e.g., \code{"k3l3"}).} } \details{ Simple \code{switch} statement selects the appropriate HWP. There are two parameters that define a Hilbert wavelet pair using the notation of Selesnick (2001,2002), \eqn{K} and \eqn{L}. Currently, the only implemented combinations \eqn{(K,L)} are (3,3), (3,5), (4,2) and (4,4). } \value{ List containing the following items: \item{L}{length of the wavelet filter} \item{h0,g0}{low-pass filter coefficients} \item{h1,g1}{high-pass filter coefficients} } \references{ Selesnick, I.W. (2001). Hilbert transform pairs of wavelet bases. \emph{IEEE Signal Processing Letters\/}~\bold{8}(6), 170--173. Selesnick, I.W. (2002). The design of approximate Hilbert transform pairs of wavelet bases. \emph{IEEE Transactions on Signal Processing\/}~\bold{50}(5), 1144--1152. } \seealso{ \code{\link{wave.filter}} } \examples{ hilbert.filter("k3l3") hilbert.filter("k3l5") hilbert.filter("k4l2") hilbert.filter("k4l4") } \author{B. Whitcher} \keyword{ts} waveslim/man/mexm.Rd0000644000176000001440000000062512453631333014147 0ustar ripleyusers\name{mexm} \alias{mexm} \title{Mexican Money Supply} \description{ Percentage changes in monthly Mexican money supply. } \usage{data(mexm) } \format{A vector containing 516 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/up.sample.Rd0000644000176000001440000000071412453631333015104 0ustar ripleyusers\name{up.sample} \alias{up.sample} \title{Upsampling of a vector} \description{ Upsamples a given vector. } \usage{up.sample(x, f, y = NA) } \arguments{ \item{x}{vector of observations} \item{f}{frequency of upsampling; e.g, 2, 4, etc.} \item{y}{value to upsample with; e.g., NA, 0, etc.} } \value{ A vector twice its length. } %\details{} \references{ Any basic signal processing text. } %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/dwt.Rd0000644000176000001440000001022512453631333013774 0ustar ripleyusers\name{dwt} \alias{dwt} \alias{dwt.nondyadic} \alias{idwt} \title{Discrete Wavelet Transform (DWT)} \description{ This function performs a level \eqn{J} decomposition of the input vector or time series using the pyramid algorithm (Mallat 1989). } \usage{ dwt(x, wf="la8", n.levels=4, boundary="periodic") dwt.nondyadic(x) } \arguments{ \item{x}{a vector or time series containing the data be to decomposed. This must be a dyadic length vector (power of 2).} \item{wf}{ Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} (Daubechies, 1992), least asymmetric family. } \item{n.levels}{ Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}{log(length(x),2)}. } \item{boundary}{ Character string specifying the boundary condition. If \code{boundary=="periodic"} the default, then the vector you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the vector beyond its boundaries is assumed to be a symmetric reflection of itself. } } \value{ Basically, a list with the following components \item{d?}{Wavelet coefficient vectors.} \item{s?}{Scaling coefficient vector.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ The code implements the one-dimensional DWT using the pyramid algorithm (Mallat, 1989). The actual transform is performed in C using pseudocode from Percival and Walden (2001). That means convolutions, not inner products, are used to apply the wavelet filters. For a non-dyadic length vector or time series, \code{dwt.nondyadic} pads with zeros, performs the orthonormal DWT on this dyadic length series and then truncates the wavelet coefficient vectors appropriately. } \references{ Daubechies, I. (1992) \emph{Ten Lectures on Wavelets}, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM: Philadelphia. Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } \seealso{ \code{\link{modwt}}, \code{\link{mra}}. } \examples{ ## Figures 4.17 and 4.18 in Gencay, Selcuk and Whitcher (2001). data(ibm) ibm.returns <- diff(log(ibm)) ## Haar ibmr.haar <- dwt(ibm.returns, "haar") names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4") ## plot partial Haar DWT for IBM data par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)") for(i in 1:4) plot.ts(up.sample(ibmr.haar[[i]], 2^i), type="h", axes=FALSE, ylab=names(ibmr.haar)[i]) plot.ts(up.sample(ibmr.haar$v4, 2^4), type="h", axes=FALSE, ylab=names(ibmr.haar)[5]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) ## LA(8) ibmr.la8 <- dwt(ibm.returns, "la8") names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4") ## must shift LA(8) coefficients ibmr.la8$w1 <- c(ibmr.la8$w1[-c(1:2)], ibmr.la8$w1[1:2]) ibmr.la8$w2 <- c(ibmr.la8$w2[-c(1:2)], ibmr.la8$w2[1:2]) for(i in names(ibmr.la8)[3:4]) ibmr.la8[[i]] <- c(ibmr.la8[[i]][-c(1:3)], ibmr.la8[[i]][1:3]) ibmr.la8$v4 <- c(ibmr.la8$v4[-c(1:2)], ibmr.la8$v4[1:2]) ## plot partial LA(8) DWT for IBM data par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)") for(i in 1:4) plot.ts(up.sample(ibmr.la8[[i]], 2^i), type="h", axes=FALSE, ylab=names(ibmr.la8)[i]) plot.ts(up.sample(ibmr.la8$v4, 2^4), type="h", axes=FALSE, ylab=names(ibmr.la8)[5]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) } \author{B. Whitcher} \keyword{ts} waveslim/man/mra.3d.Rd0000644000176000001440000000374512453631333014273 0ustar ripleyusers\name{mra.3d} \alias{mra.3d} \title{Three Dimensional Multiresolution Analysis} \description{ This function performs a level \eqn{J} additive decomposition of the input array using the pyramid algorithm (Mallat 1989). } \usage{mra.3d(x, wf, J=4, method="modwt", boundary="periodic") } \arguments{ \item{x}{A three-dimensional array containing the data be to decomposed. This must be have dyadic length in all three dimensions (but not necessarily the same) for \code{method="dwt"}.} \item{wf}{Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} least asymmetric family.} \item{J}{Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}{log(length(x),2)}.} \item{method}{Either \code{"dwt"} or \code{"modwt"}.} \item{boundary}{Character string specifying the boundary condition. If \code{boundary=="periodic"} the default and only method implemented, then the matrix you decompose is assumed to be periodic on its defined interval.} } \details{ This code implements a three-dimensional multiresolution analysis by performing the one-dimensional pyramid algorithm (Mallat 1989) on each dimension of the input array. Either the DWT or MODWT may be used to compute the multiresolution analysis, which is an additive decomposition of the original array. } \value{ List structure containing the filter triplets associated with the multiresolution analysis. } \references{ Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Mallat, S. G. (1998) \emph{A Wavelet Tour of Signal Processing}, Academic Press. } \seealso{ \code{\link{dwt.3d}}, \code{\link{modwt.3d}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/Farras.Rd0000644000176000001440000000166712453631333014426 0ustar ripleyusers\name{Farras} \alias{farras} \alias{FSfarras} \title{Farras nearly symmetric filters} \description{ Farras nearly symmetric filters for orthogonal 2-channel perfect reconstruction filter bank and Farras filters organized for the dual-tree complex DWT. } \usage{ farras() FSfarras() } \arguments{ None. } \value{ \item{af}{List (\eqn{i=1,2}) - analysis filters for tree \eqn{i}} \item{sf}{List (\eqn{i=1,2}) - synthesis filters for tree \eqn{i}} } %\details{} \references{ A. F. Abdelnour and I. W. Selesnick. \dQuote{Nearly symmetric orthogonal wavelet bases}, Proc. IEEE Int. Conf. Acoust., Speech, Signal Processing (ICASSP), May 2001. WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY\cr \url{http://taco.poly.edu/WaveletSoftware/} } \seealso{ \code{\link{afb}}, \code{\link{dualtree}}, \code{\link{dualfilt1}}. } %\examples{} \author{Matlab: S. Cai, K. Li and I. Selesnick; R port: Brandon Whitcher} \keyword{ts} waveslim/man/exchange.Rd0000644000176000001440000000107012453631333014756 0ustar ripleyusers\name{exchange} \alias{exchange} \title{Exchange Rates Between the Deutsche Mark, Japanese Yen and U.S. Dollar} \description{ Monthly foreign exchange rates for the Deutsche Mark - U.S. Dollar (DEM-USD) and Japanese Yen - U.S. Dollar (JPY-USD) starting in 1970. } \usage{data(exchange) } \format{A bivariate time series containing 348 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/wavelet.filter.Rd0000644000176000001440000000432312453631333016133 0ustar ripleyusers\name{wavelet.filter} \alias{wavelet.filter} \title{Higher-Order Wavelet Filters} \description{ Create a wavelet filter at arbitrary scale. } \usage{wavelet.filter(wf.name, filter.seq = "L", n = 512) } \arguments{ \item{wf.name}{Character string of wavelet filter.} \item{filter.seq}{Character string of filter sequence. \code{H} means high-pass filtering and \code{L} means low-pass filtering. Sequence is read from right to left.} \item{n}{Length of zero-padded filter. Frequency resolution will be \code{n}/2+1.} } \value{ Vector of wavelet coefficients. } \details{ Uses \code{cascade} subroutine to compute higher-order wavelet coefficient vector from a given filtering sequence. } \references{ Bruce, A. and H.-Y. Gao (1996). \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. Doroslovacki, M. L. (1998) On the least asymmetric wavelets, \emph{IEEE Transactions on Signal Processing}, \bold{46}, No. 4, 1125-1130. Daubechies, I. (1992) \emph{Ten Lectures on Wavelets}, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM: Philadelphia. Morris and Peravali (1999) Minimum-bandwidth discrete-time wavelets, \emph{Signal Processing}, \bold{76}, No. 2, 181-193. Nielsen, M. (2001) On the Construction and Frequency Localization of Finite Orthogonal Quadrature Filters, \emph{Journal of Approximation Theory}, \bold{108}, No. 1, 36-52. } \seealso{ \code{\link{squared.gain}}, \code{\link{wave.filter}}. } \examples{ ## Figure 4.14 in Gencay, Selcuk and Whitcher (2001) par(mfrow=c(3,1), mar=c(5-2,4,4-1,2)) f.seq <- "HLLLLL" plot(c(rep(0,33), wavelet.filter("mb4", f.seq), rep(0,33)), type="l", xlab="", ylab="", main="D(4) in black, MB(4) in red") lines(c(rep(0,33), wavelet.filter("d4", f.seq), rep(0,33)), col=2) plot(c(rep(0,35), -wavelet.filter("mb8", f.seq), rep(0,35)), type="l", xlab="", ylab="", main="D(8) in black, -MB(8) in red") lines(c(rep(0,35), wavelet.filter("d8", f.seq), rep(0,35)), col=2) plot(c(rep(0,39), wavelet.filter("mb16", f.seq), rep(0,39)), type="l", xlab="", ylab="", main="D(16) in black, MB(16) in red") lines(c(rep(0,39), wavelet.filter("d16", f.seq), rep(0,39)), col=2) } \author{B. Whitcher} \keyword{ts} waveslim/man/fb.Rd0000644000176000001440000000577712453631333013605 0ustar ripleyusers\name{Dual-tree Filter Banks} \alias{afb} \alias{afb2D} \alias{afb2D.A} \alias{sfb} \alias{sfb2D} \alias{sfb2D.A} \title{Filter Banks for Dual-Tree Wavelet Transforms} \description{ Analysis and synthesis filter banks used in dual-tree wavelet algorithms. } \usage{ afb(x, af) afb2D(x, af1, af2 = NULL) afb2D.A(x, af, d) sfb(lo, hi, sf) sfb2D(lo, hi, sf1, sf2 = NULL) sfb2D.A(lo, hi, sf, d) } \arguments{ \item{x}{vector or matrix of observations} \item{af}{analysis filters. First element of the list is the low-pass filter, second element is the high-pass filter.} \item{af1,af2}{analysis filters for the first and second dimension of a 2D array.} \item{sf}{synthesis filters. First element of the list is the low-pass filter, second element is the high-pass filter.} \item{sf1,sf2}{synthesis filters for the first and second dimension of a 2D array.} \item{d}{dimension of filtering (d = 1 or 2)} \item{lo}{low-frequecy coefficients} \item{hi}{high-frequency coefficients} } \details{ The functions \code{afb2D.A} and \code{sfb2D.A} implement the convolutions, either for analysis or synthesis, in one dimension only. Thus, they are the workhorses of \code{afb2D} and \code{sfb2D}. The output for the analysis filter bank along one dimension (\code{afb2D.A}) is a list with two elements \describe{ \item{lo}{low-pass subband} \item{hi}{high-pass subband} } where the dimension of analysis will be half its original length. The output for the synthesis filter bank along one dimension (\code{sfb2D.A}) will be the output array, where the dimension of synthesis will be twice its original length. } \value{ In one dimension the output for the analysis filter bank (\code{afb}) is a list with two elements \item{lo}{Low frequecy output} \item{hi}{High frequency output} and the output for the synthesis filter bank (\code{sfb}) is the output signal. In two dimensions the output for the analysis filter bank (\code{afb2D}) is a list with four elements \item{lo}{low-pass subband} \item{hi[[1]]}{'lohi' subband} \item{hi[[2]]}{'hilo' subband} \item{hi[[3]]}{'hihi' subband} and the output for the synthesis filter bank (\code{sfb2D}) is the output array. } \references{ WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY\cr \url{http://taco.poly.edu/WaveletSoftware/} } %\seealso{} \examples{ ## EXAMPLE: afb, sfb af = farras()$af sf = farras()$sf x = rnorm(64) x.afb = afb(x, af) lo = x.afb$lo hi = x.afb$hi y = sfb(lo, hi, sf) err = x - y max(abs(err)) ## EXAMPLE: afb2D, sfb2D x = matrix(rnorm(32*64), 32, 64) af = farras()$af sf = farras()$sf x.afb2D = afb2D(x, af, af) lo = x.afb2D$lo hi = x.afb2D$hi y = sfb2D(lo, hi, sf, sf) err = x - y max(abs(err)) ## Example: afb2D.A, sfb2D.A x = matrix(rnorm(32*64), 32, 64) af = farras()$af sf = farras()$sf x.afb2D.A = afb2D.A(x, af, 1) lo = x.afb2D.A$lo hi = x.afb2D.A$hi y = sfb2D.A(lo, hi, sf, 1) err = x - y max(abs(err)) } \author{Matlab: S. Cai, K. Li and I. Selesnick; R port: B. Whitcher} \keyword{ts} waveslim/man/Thresholding.Rd0000644000176000001440000000451012453631333015630 0ustar ripleyusers\name{Thresholding} \alias{Thresholding} \alias{da.thresh} \alias{hybrid.thresh} \alias{manual.thresh} \alias{sure.thresh} \alias{universal.thresh} \alias{universal.thresh.modwt} \alias{bishrink} \alias{soft} \title{Wavelet Shrinkage via Thresholding} \description{ Perform wavelet shrinkage using data-analytic, hybrid SURE, manual, SURE, or universal thresholding. } \usage{ da.thresh(wc, alpha = .05, max.level = 4, verbose = FALSE, return.thresh = FALSE) hybrid.thresh(wc, max.level = 4, verbose = FALSE, seed = 0) manual.thresh(wc, max.level = 4, value, hard = TRUE) sure.thresh(wc, max.level = 4, hard = TRUE) universal.thresh(wc, max.level = 4, hard = TRUE) universal.thresh.modwt(wc, max.level = 4, hard = TRUE) } \arguments{ \item{wc}{wavelet coefficients} \item{alpha}{level of the hypothesis tests} \item{max.level}{maximum level of coefficients to be affected by threshold} \item{verbose}{if \code{verbose=TRUE} then information is printed to the screen} \item{value}{threshold value (only utilized in \code{manual.thresh})} \item{hard}{Boolean value, if \code{hard=F} then soft thresholding is used} \item{seed}{sets random seed (only utilized in \code{hybrid.thresh})} \item{return.thresh}{if \code{return.thresh=TRUE} then the vector of threshold values is returned, otherwise the surviving wavelet coefficients are returned} } \value{ The default output is a list structure, the same length as was input, containing only those wavelet coefficients surviving the threshold. } \details{ An extensive amount of literature has been written on wavelet shrinkage. The functions here represent the most basic approaches to the problem of nonparametric function estimation. See the references for further information. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Ogden, R. T. (1996) \emph{Essential Wavelets for Statistical Applications and Data Analysis}, Birkhauser. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. Vidakovic, B. (1999) \emph{Statistical Modeling by Wavelets}, John Wiley \& Sons. } %\seealso{} %\examples{} \author{B. Whitcher (some code taken from R. Todd Ogden)} \keyword{ts} waveslim/man/rotcumvar.Rd0000644000176000001440000000231712453631333015223 0ustar ripleyusers\name{rotcumvar} \alias{rotcumvar} \title{Rotated Cumulative Variance} \description{ Provides the normalized cumulative sums of squares from a sequence of coefficients with the diagonal line removed. } \usage{rotcumvar(x) } \arguments{ \item{x}{vector of coefficients to be cumulatively summed (missing values excluded)} } \value{Vector of coefficients that are the sumulative sum of squared input coefficients. } \details{ The rotated cumulative variance, when plotted, provides a qualitative way to study the time dependence of the variance of a series. If the variance is stationary over time, then only small deviations from zero should be present. If on the other hand the variance is non-stationary, then large departures may exist. Formal hypothesis testing may be performed based on boundary crossings of Brownian bridge processes. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/hilbert.Rd0000644000176000001440000000301212453631333014623 0ustar ripleyusers\name{Hilbert} \alias{dwt.hilbert} \alias{dwt.hilbert.nondyadic} \alias{idwt.hilbert} \alias{modwt.hilbert} \alias{imodwt.hilbert} \alias{modwpt.hilbert} \title{Discrete Hilbert Wavelet Transforms} \description{ The discrete Hilbert wavelet transforms (DHWTs) for seasonal and time-varying time series analysis. Transforms include the usual orthogonal (decimated), maximal-overlap (non-decimated) and maximal-overlap packet transforms. } \usage{ dwt.hilbert(x, wf, n.levels=4, boundary="periodic", ...) dwt.hilbert.nondyadic(x, ...) idwt.hilbert(y) modwt.hilbert(x, wf, n.levels=4, boundary="periodic", ...) imodwt.hilbert(y) modwpt.hilbert(x, wf, n.levels=4, boundary="periodic") } \arguments{ \item{x}{Real-valued time series or vector of observations.} \item{wf}{Hilbert wavelet pair} \item{n.levels}{Number of levels (depth) of the wavelet transform.} \item{boundary}{Boundary treatment, currently only \code{periodic} and \code{reflection}.} \item{y}{Hilbert wavelet transform object (list).} \item{\ldots}{Additional parametes to be passed on.} } %\value{} %\details{} \references{ Selesnick, I. (200X). \emph{IEEE Signal Processing Magazine} Selesnick, I. (200X). \emph{IEEE Transactions in Signal Processing} Whither, B. and P.F. Craigmile (2004). Multivariate Spectral Analysis Using Hilbert Wavelet Pairs, \emph{International Journal of Wavelets, Multiresolution and Information Processing}, to appear. } \seealso{ \code{\link{hilbert.filter}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/bandpass.Rd0000644000176000001440000000265012453631333014774 0ustar ripleyusers\name{Band-pass variance} \alias{bandpass.fdp} \alias{bandpass.spp} \alias{bandpass.spp2} \alias{bandpass.var.spp} \title{Bandpass Variance for Long-Memory Processes} \description{ Computes the band-pass variance for fractional difference (FD) or seasonal persistent (SP) processes using numeric integration of their spectral density function. } \usage{ bandpass.fdp(a, b, d) bandpass.spp(a, b, d, fG) bandpass.spp2(a, b, d1, f1, d2, f2) bandpass.var.spp(delta, fG, J, Basis, Length) } \arguments{ \item{a}{Left-hand boundary for the definite integral.} \item{b}{Right-hand boundary for the definite integral.} \item{d,delta,d1,d2}{Fractional difference parameter.} \item{fG,f1,f2}{Gegenbauer frequency.} \item{J}{Depth of the wavelet transform.} \item{Basis}{Logical vector representing the adaptive basis.} \item{Length}{Number of elements in Basis.} } \value{ Band-pass variance for the FD or SP process between \eqn{a} and \eqn{b}. } \details{ See references. } \references{ McCoy, E. J., and A. T. Walden (1996) Wavelet analysis and synthesis of stationary long-memory processes, \emph{Journal for Computational and Graphical Statistics}, \bold{5}, No. 1, 26-56. Whitcher, B. (2001) Simulating Gaussian stationary processes with unbounded spectra, \emph{Journal for Computational and Graphical Statistics}, \bold{10}, No. 1, 112-134. } %\seealso{} %\examples{} \author{Brandon Whitcher} \keyword{ts} waveslim/man/spp.mle.Rd0000644000176000001440000000353312453631333014560 0ustar ripleyusers\name{spp.mle} \alias{spp.mle} \alias{spp2.mle} \title{Wavelet-based Maximum Likelihood Estimation for Seasonal Persistent Processes} \description{ Parameter estimation for a seasonal persistent (seasonal long-memory) process is performed via maximum likelihood on the wavelet coefficients. } \usage{spp.mle(y, wf, J=log(length(y),2)-1, p=0.01, frac=1) spp2.mle(y, wf, J=log(length(y),2)-1, p=0.01, dyadic=TRUE, frac=1) } \arguments{ \item{y}{Not necessarily dyadic length time series.} \item{wf}{Name of the wavelet filter to use in the decomposition. See \code{\link{wave.filter}} for those wavelet filters available.} \item{J}{Depth of the discrete wavelet packet transform.} \item{p}{Level of significance for the white noise testing procedure.} \item{dyadic}{Logical parameter indicating whether or not the original time series is dyadic in length.} \item{frac}{Fraction of the time series that should be used in constructing the likelihood function.} } \value{ List containing the maximum likelihood estimates (MLEs) of \eqn{\delta}, \eqn{f_G} and \eqn{\sigma^2}, along with the value of the likelihood for those estimates. } \details{ The variance-covariance matrix of the original time series is approximated by its wavelet-based equivalent. A Whittle-type likelihood is then constructed where the sums of squared wavelet coefficients are compared to bandpass filtered version of the true spectral density function. Minimization occurs for the fractional difference parameter \eqn{d} and the Gegenbauer frequency \eqn{f_G}, while the innovations variance is subsequently estimated. } \references{ Whitcher, B. (2004) Wavelet-based estimation for seasonal long-memory processes, \emph{Technometrics}, \bold{46}, No. 2, 225-238. } \seealso{ \code{\link{fdp.mle}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/kobe.Rd0000644000176000001440000000102712453631333014116 0ustar ripleyusers\name{kobe} \alias{kobe} \title{1995 Kobe Earthquake Data} \description{ Seismograph (vertical acceleration, nm/sq.sec) of the Kobe earthquake, recorded at Tasmania University, HobarTRUE, Australia on 16 January 1995 beginning at 20:56:51 (GMTRUE) and continuing for 51 minutes at 1 second intervals. } \usage{data(kobe) } \format{A vector containing 3048 observations. } \source{Data management centre, Washington University. } \references{ \url{http://www-personal.buseco.monash.edu.au/~hyndman/TSDL/} } \keyword{datasets} waveslim/man/dau.Rd0000644000176000001440000000077112453631333013754 0ustar ripleyusers\name{dau} \alias{dau} \title{Digital Photograph of Ingrid Daubechies} \description{ A digital photograph of Ingrid Daubechies taken at the 1993 AMS winter meetings in San Antonio, Texas. The photograph was taken by David Donoho with a Canon XapShot video still frame camera. } \usage{data(dau) } \format{A 256 \eqn{\times}{x} 256 matrix. } \source{S+WAVELETS. } \references{ Bruce, A., and H.-Y. Gao (1996) \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. } \keyword{datasets} waveslim/man/unemploy.Rd0000644000176000001440000000064412453631333015052 0ustar ripleyusers\name{unemploy} \alias{unemploy} \title{U.S. Unemployment} \description{ Monthly U.S. unemployment figures from 1948:1 to 1999:12. } \usage{data(unemploy) } \format{A vector containing 624 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/phase.shift.Rd0000644000176000001440000000240612453631333015414 0ustar ripleyusers\name{phase.shift} \alias{phase.shift} \alias{phase.shift.packet} \title{Phase Shift Wavelet Coefficients} \description{ Wavelet coefficients are circularly shifted by the amount of phase shift induced by the wavelet transform. } \usage{phase.shift(z, wf, inv = FALSE) phase.shift.packet(z, wf, inv = FALSE) } \arguments{ \item{z}{DWT object} \item{wf}{character string; wavelet filter used in DWT} \item{inv}{Boolean variable; if \code{inv=TRUE} then the inverse phase shift is applied} } \value{ DWT (DWPT) object with coefficients circularly shifted. } \details{ The center-of-energy argument of Hess-Nielsen and Wickerhauser (1996) is used to provide a flexible way to circularly shift wavelet coefficients regardless of the wavelet filter used. The results are not identical to those used by Percival and Walden (2000), but are more flexible. \code{phase.shift.packet} is not yet implemented fully. } \references{ Hess-Nielsen, N. and M. V. Wickerhauser (1996) Wavelets and time-frequency analysis, \emph{Proceedings of the IEEE}, \bold{84}, No. 4, 523-540. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/modwt.3d.Rd0000644000176000001440000000121712453631333014636 0ustar ripleyusers\name{modwt.3d} \alias{modwt.3d} \alias{imodwt.3d} \title{Three Dimensional Separable Maximal Ovelrap Discrete Wavelet Transform} \description{ Three-dimensional separable maximal overlap discrete wavelet transform (MODWT). } \usage{ modwt.3d(x, wf, J = 4, boundary = "periodic") imodwt.3d(y) } \arguments{ \item{x}{input array} \item{wf}{name of the wavelet filter to use in the decomposition} \item{J}{depth of the decomposition} \item{boundary}{only \code{"periodic"} is currently implemented} \item{y}{an object of class \code{modwt.3d}} } %\value{} %\details{} %\references{} %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/dwpt.2d.Rd0000644000176000001440000000525012453631333014462 0ustar ripleyusers\name{dwpt.2d} \alias{dwpt.2d} \alias{idwpt.2d} %\alias{modwpt.2d} \title{(Inverse) Discrete Wavelet Packet Transforms in Two Dimensions} \description{ All possible filtering combinations (low- and high-pass) are performed to decompose a matrix or image. The resulting coefficients are associated with a quad-tree structure corresponding to a partitioning of the two-dimensional frequency plane. } \usage{dwpt.2d(x, wf="la8", J=4, boundary="periodic") idwpt.2d(y, y.basis) %modwpt.2d(x, wf="la8", J=4, boundary="periodic") } \arguments{ \item{x}{ a matrix or image containing the data be to decomposed. This ojbect must be dyadic (power of 2) in length in each dimension. } \item{wf}{ Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} (Daubechies, 1992), least asymmetric family. } \item{J}{ Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}. } \item{boundary}{ Character string specifying the boundary condition. If \code{boundary=="periodic"} the default, then the vector you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the vector beyond its boundaries is assumed to be a symmetric reflection of itself. } \item{y}{\code{dwpt.2d} object (list-based structure of matrices)} \item{y.basis}{Boolean vector, the same length as \eqn{y}, where \code{TRUE} means the basis tensor should be used in the reconstruction.} } \value{ Basically, a list with the following components \item{w?.?-w?.?}{Wavelet coefficient matrices (images). The first index is associated with the scale of the decomposition while the second is associated with the frequency partition within that level. The left and right strings, separated by the dash `-', correspond to the first \eqn{(x)} and second \eqn{(y)} dimensions.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ The code implements the two-dimensional DWPT using the pyramid algorithm of Mallat (1989). } \references{ Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Wickerhauser, M. V. (1994) \emph{Adapted Wavelet Analysis from Theory to Software}, A K Peters. } \seealso{ \code{\link{dwt.2d}}, \code{\link{modwt.2d}}, \code{\link{wave.filter}}. } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/wpt.test.Rd0000644000176000001440000000340312453631333014766 0ustar ripleyusers\name{wpt.test} \alias{cpgram.test} \alias{css.test} \alias{entropy.test} \alias{portmanteau.test} \title{Testing the Wavelet Packet Tree for White Noise} \description{ A wavelet packet tree, from the discrete wavelet packet transform (DWPT), is tested node-by-node for white noise. This is the first step in selecting an orthonormal basis for the DWPT. } \usage{cpgram.test(y, p = 0.05, taper = 0.1) css.test(y) entropy.test(y) portmanteau.test(y, p = 0.05, type = "Box-Pierce") } \arguments{ \item{y}{wavelet packet tree (from the DWPT)} \item{p}{significance level} \item{taper}{weight of cosine bell taper (\code{cpgram.test} only)} \item{type}{\code{"Box-Pierce"} and \code{other} recognized (\code{portmanteau.test} only)} } \value{ Boolean vector of the same length as the number of nodes in the wavelet packet tree. } \details{ Top-down recursive testing of the wavelet packet tree is } \references{ Brockwell and Davis (1991) \emph{Time Series: Theory and Methods}, (2nd. edition), Springer-Verlag. Brown, Durbin and Evans (1975) Techniques for testing the constancy of regression relationships over time, \emph{Journal of the Royal Statistical Society B}, \bold{37}, 149-163. Percival, D. B., and A. T. Walden (1993) \emph{Spectral Analysis for Physical Applications: Multitaper and Conventional Univariate Techniques}, Cambridge University Press. } \seealso{ \code{\link{ortho.basis}}. } \examples{ data(mexm) J <- 6 wf <- "la8" mexm.dwpt <- dwpt(mexm[-(1:4)], wf, J) ## Not implemented yet ## plot.dwpt(x.dwpt, J) mexm.dwpt.bw <- dwpt.brick.wall(mexm.dwpt, wf, 6, method="dwpt") mexm.tree <- ortho.basis(portmanteau.test(mexm.dwpt.bw, p=0.025)) ## Not implemented yet ## plot.basis(mexm.tree) } \author{B. Whitcher} \keyword{ts} waveslim/man/shift.2d.Rd0000644000176000001440000000316412453631333014623 0ustar ripleyusers\name{shift.2d} \alias{shift.2d} \title{Circularly Shift Matrices from a 2D MODWT} \description{ Compute phase shifts for wavelet sub-matrices based on the ``center of energy'' argument of Hess-Nielsen and Wickerhauser (1996). } \usage{shift.2d(z, inverse=FALSE) } \arguments{ \item{z}{Two-dimensional MODWT object} % \item{wf}{Character string for wavelet filter.} \item{inverse}{Boolean value on whether to perform the forward or inverse operation.} } \value{ Two-dimensional MODWT object with circularly shifted coefficients. } \details{ The "center of energy" technique of Wickerhauser and Hess-Nielsen (1996) is employed to find circular shifts for the wavelet sub-matrices such that the coefficients are aligned with the original series. This corresponds to applying a (near) linear-phase filtering operation. } \references{ Hess-Nielsen, N. and M. V. Wickerhauser (1996) Wavelets and time-frequency analysis, \emph{Proceedings of the IEEE}, \bold{84}, No. 4, 523-540. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } \seealso{ \code{\link{phase.shift}}, \code{\link{modwt.2d}}. } \examples{ n <- 512 G1 <- G2 <- dnorm(seq(-n/4, n/4, length=n)) G <- 100 * zapsmall(outer(G1, G2)) G <- modwt.2d(G, wf="la8", J=6) k <- 50 xr <- yr <- trunc(n/2) + (-k:k) par(mfrow=c(3,3), mar=c(1,1,2,1), pty="s") for (j in names(G)[1:9]) { image(G[[j]][xr,yr], col=rainbow(64), axes=FALSE, main=j) } Gs <- shift.2d(G) for (j in names(G)[1:9]) { image(Gs[[j]][xr,yr], col=rainbow(64), axes=FALSE, main=j) } } \author{Brandon Whitcher} \keyword{ts} waveslim/man/mra.Rd0000644000176000001440000000663413622226527013772 0ustar ripleyusers\name{mra} \alias{mra} \title{Multiresolution Analysis of Time Series} \description{ This function performs a level \eqn{J} additive decomposition of the input vector or time series using the pyramid algorithm (Mallat 1989). } \usage{mra(x, wf = "la8", J = 4, method = "modwt", boundary = "periodic") } \arguments{ \item{x}{A vector or time series containing the data be to decomposed. This must be a dyadic length vector (power of 2) for \code{method="dwt"}.} \item{wf}{Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} least asymmetric family.} \item{J}{Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}{log(length(x),2)}.} \item{method}{Either \code{"dwt"} or \code{"modwt"}.} \item{boundary}{Character string specifying the boundary condition. If \code{boundary=="periodic"} the default, then the vector you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the vector beyond its boundaries is assumed to be a symmetric reflection of itself.} } \value{ Basically, a list with the following components \item{D?}{Wavelet detail vectors.} \item{S?}{Wavelet smooth vector.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ This code implements a one-dimensional multiresolution analysis introduced by Mallat (1989). Either the DWT or MODWT may be used to compute the multiresolution analysis, which is an additive decomposition of the original time series. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } \seealso{ \code{\link{dwt}}, \code{\link{modwt}}. } \examples{ ## Easy check to see if it works... x <- rnorm(32) x.mra <- mra(x) ## IGNORE_RDIFF_BEGIN sum(x - apply(matrix(unlist(x.mra), nrow=32), 1, sum))^2 ## IGNORE_RDIFF_END ## Figure 4.19 in Gencay, Selcuk and Whitcher (2001) data(ibm) ibm.returns <- diff(log(ibm)) ibm.volatility <- abs(ibm.returns) ## Haar ibmv.haar <- mra(ibm.volatility, "haar", 4, "dwt") names(ibmv.haar) <- c("d1", "d2", "d3", "d4", "s4") ## LA(8) ibmv.la8 <- mra(ibm.volatility, "la8", 4, "dwt") names(ibmv.la8) <- c("d1", "d2", "d3", "d4", "s4") ## plot multiresolution analysis of IBM data par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.volatility, axes=FALSE, ylab="", main="(a)") for(i in 1:5) plot.ts(ibmv.haar[[i]], axes=FALSE, ylab=names(ibmv.haar)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) plot.ts(ibm.volatility, axes=FALSE, ylab="", main="(b)") for(i in 1:5) plot.ts(ibmv.la8[[i]], axes=FALSE, ylab=names(ibmv.la8)[i]) axis(side=1, at=seq(0,368,by=23), labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) } \author{B. Whitcher} \keyword{ts} waveslim/man/spin.covariance.Rd0000644000176000001440000000473712453631333016273 0ustar ripleyusers\name{spin.covariance} \alias{spin.covariance} \alias{spin.correlation} \title{Compute Wavelet Cross-Covariance Between Two Time Series} \description{ Computes wavelet cross-covariance or cross-correlation between two time series. } \usage{spin.covariance(x, y, lag.max = NA) spin.correlation(x, y, lag.max = NA) } \arguments{ \item{x}{first time series} \item{y}{second time series, same length as \code{x}} \item{lag.max}{maximum lag to compute cross-covariance (correlation)} } \value{ List structure holding the wavelet cross-covariances (correlations) according to scale. } \details{ See references. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Whitcher, B., P. Guttorp and D. B. Percival (2000) Wavelet analysis of covariance with application to atmospheric time series, \emph{Journal of Geophysical Research}, \bold{105}, No. D11, 14,941-14,962. } \seealso{ \code{\link{wave.covariance}}, \code{\link{wave.correlation}}. } \examples{ ## Figure 7.9 from Gencay, Selcuk and Whitcher (2001) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) wf <- "d4" demusd.modwt <- modwt(returns[,"DEM.USD"], wf, 8) demusd.modwt.bw <- brick.wall(demusd.modwt, wf) jpyusd.modwt <- modwt(returns[,"JPY.USD"], wf, 8) jpyusd.modwt.bw <- brick.wall(jpyusd.modwt, wf) n <- dim(returns)[1] J <- 6 lmax <- 36 returns.cross.cor <- NULL for(i in 1:J) { blah <- spin.correlation(demusd.modwt.bw[[i]], jpyusd.modwt.bw[[i]], lmax) returns.cross.cor <- cbind(returns.cross.cor, blah) } returns.cross.cor <- ts(as.matrix(returns.cross.cor), start=-36, freq=1) dimnames(returns.cross.cor) <- list(NULL, paste("Level", 1:J)) lags <- length(-lmax:lmax) lower.ci <- tanh(atanh(returns.cross.cor) - qnorm(0.975) / sqrt(matrix(trunc(n/2^(1:J)), nrow=lags, ncol=J, byrow=TRUE) - 3)) upper.ci <- tanh(atanh(returns.cross.cor) + qnorm(0.975) / sqrt(matrix(trunc(n/2^(1:J)), nrow=lags, ncol=J, byrow=TRUE) - 3)) par(mfrow=c(3,2), las=1, pty="m", mar=c(5,4,4,2)+.1) for(i in J:1) { plot(returns.cross.cor[,i], ylim=c(-1,1), xaxt="n", xlab="Lag (months)", ylab="", main=dimnames(returns.cross.cor)[[2]][i]) axis(side=1, at=seq(-36, 36, by=12)) lines(lower.ci[,i], lty=1, col=2) lines(upper.ci[,i], lty=1, col=2) abline(h=0,v=0) } } \author{B. Whitcher} \keyword{ts} waveslim/man/squared.gain.Rd0000644000176000001440000000375112453631333015565 0ustar ripleyusers\name{squared.gain} \alias{squared.gain} \title{Squared Gain Function of a Filter} \description{ Produces the modulus squared of the Fourier transform for a given filtering sequence. } \usage{squared.gain(wf.name, filter.seq = "L", n = 512) } \arguments{ \item{wf.name}{Character string of wavelet filter.} \item{filter.seq}{Character string of filter sequence. \code{H} means high-pass filtering and \code{L} means low-pass filtering. Sequence is read from right to left.} \item{n}{Length of zero-padded filter. Frequency resolution will be \code{n}/2+1.} } \value{ Squared gain function. } \details{ Uses \code{cascade} subroutine to compute the squared gain function from a given filtering sequence. } %\references{} \seealso{ \code{\link{wave.filter}}, \code{\link{wavelet.filter}}. } \examples{ par(mfrow=c(2,2)) f.seq <- "H" plot(0:256/512, squared.gain("d4", f.seq), type="l", ylim=c(0,2), xlab="frequency", ylab="L = 4", main="Level 1") lines(0:256/512, squared.gain("fk4", f.seq), col=2) lines(0:256/512, squared.gain("mb4", f.seq), col=3) abline(v=c(1,2)/4, lty=2) legend(-.02, 2, c("Daubechies", "Fejer-Korovkin", "Minimum-Bandwidth"), lty=1, col=1:3, bty="n", cex=1) f.seq <- "HL" plot(0:256/512, squared.gain("d4", f.seq), type="l", ylim=c(0,4), xlab="frequency", ylab="", main="Level 2") lines(0:256/512, squared.gain("fk4", f.seq), col=2) lines(0:256/512, squared.gain("mb4", f.seq), col=3) abline(v=c(1,2)/8, lty=2) f.seq <- "H" plot(0:256/512, squared.gain("d8", f.seq), type="l", ylim=c(0,2), xlab="frequency", ylab="L = 8", main="") lines(0:256/512, squared.gain("fk8", f.seq), col=2) lines(0:256/512, squared.gain("mb8", f.seq), col=3) abline(v=c(1,2)/4, lty=2) f.seq <- "HL" plot(0:256/512, squared.gain("d8", f.seq), type="l", ylim=c(0,4), xlab="frequency", ylab="", main="") lines(0:256/512, squared.gain("fk8", f.seq), col=2) lines(0:256/512, squared.gain("mb8", f.seq), col=3) abline(v=c(1,2)/8, lty=2) } \author{B. Whitcher} \keyword{ts} waveslim/man/cpi.Rd0000644000176000001440000000063512453631333013755 0ustar ripleyusers\name{cpi} \alias{cpi} \title{U.S. Consumer Price Index} \description{ Monthly U.S. consumer price index from 1948:1 to 1999:12. } \usage{data(cpi) } \format{A vector containing 624 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. } \keyword{datasets} waveslim/man/hosking.sim.Rd0000644000176000001440000000275712453631333015442 0ustar ripleyusers\name{hosking.sim} \alias{hosking.sim} \title{Generate Stationary Gaussian Process Using Hosking's Method} \description{ Uses exact time-domain method from Hosking (1984) to generate a simulated time series from a specified autocovariance sequence. } \usage{hosking.sim(n, acvs) } \arguments{ \item{n}{Length of series.} \item{acvs}{Autocovariance sequence of series with which to generate, must be of length at least \code{n}.} } \value{ Length \code{n} time series from true autocovariance sequence \code{acvs}. } %\details{} \references{ Hosking, J. R. M. (1984) Modeling persistence in hydrological time series using fractional differencing, \emph{Water Resources Research}, \bold{20}, No. 12, 1898-1908. Percival, D. B. (1992) Simulating Gaussian random processes with specified spectra, \emph{Computing Science and Statistics}, \bold{22}, 534-538. } %\seealso{} \examples{ dB <- function(x) 10 * log10(x) per <- function (z) { n <- length(z) (Mod(fft(z))^2/(2 * pi * n))[1:(n\%/\%2 + 1)] } spp.sdf <- function(freq, delta, omega) abs(2 * (cos(2*pi*freq) - cos(2*pi*omega)))^(-2*delta) data(acvs.andel8) n <- 1024 \dontrun{ z <- hosking.sim(n, acvs.andel8[,2]) per.z <- 2 * pi * per(z) par(mfrow=c(2,1), las=1) plot.ts(z, ylab="", main="Realization of a Seasonal Long-Memory Process") plot(0:(n/2)/n, dB(per.z), type="l", xlab="Frequency", ylab="dB", main="Periodogram") lines(0:(n/2)/n, dB(spp.sdf(0:(n/2)/n, .4, 1/12)), col=2) } } \author{Brandon Whitcher} \keyword{ts} waveslim/man/blocks.Rd0000644000176000001440000000066712453631333014464 0ustar ripleyusers\name{blocks} \alias{blocks} \title{A Piecewise-Constant Function} \description{ \deqn{blocks(x) = \sum_{j=1}^{11}(1 + {\rm sign}(x-p_j)) h_j / 2}{% blocks(x) = sum[j=1,11] (1 + sign(x - p_j)) h_j/2} } \usage{data(blocks) } \format{A vector containing 512 observations. } \source{S+WAVELETS. } \references{ Bruce, A., and H.-Y. Gao (1996) \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. } \keyword{datasets} waveslim/man/sine.taper.Rd0000644000176000001440000000115112453631333015244 0ustar ripleyusers\name{sine.taper} \alias{sine.taper} \title{Computing Sinusoidal Data Tapers} \description{ Computes sinusoidal data tapers directly from equations. } \usage{sine.taper(n, k) } \arguments{ \item{n}{length of data taper(s)} \item{k}{number of data tapers} } \value{ A vector or matrix of data tapers (cols = tapers). } \details{ See reference. } \references{ Riedel, K. S. and A. Sidorenko (1995) Minimum bias multiple taper spectral estimation, \emph{IEEE Transactions on Signal Processing}, \bold{43}, 188-195. } \seealso{ \code{\link{dpss.taper}}. } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/phase.shift.hilbert.Rd0000644000176000001440000000200112453631333017033 0ustar ripleyusers\name{phase.shift.hilbert} \alias{phase.shift.hilbert} \alias{phase.shift.hilbert.packet} \title{Phase Shift for Hilbert Wavelet Coefficients} \description{ Wavelet coefficients are circularly shifted by the amount of phase shift induced by the discrete Hilbert wavelet transform. } \usage{ phase.shift.hilbert(x, wf) phase.shift.hilbert.packet(x, wf) } \arguments{ \item{x}{Discete Hilbert wavelet transform (DHWT) object.} \item{wf}{character string; Hilbert wavelet pair used in DHWT} } \value{ DHWT (DHWPT) object with coefficients circularly shifted. } \details{ The "center-of-energy" argument of Hess-Nielsen and Wickerhauser (1996) is used to provide a flexible way to circularly shift wavelet coefficients regardless of the wavelet filter used. } \references{ Hess-Nielsen, N. and M. V. Wickerhauser (1996) Wavelets and time-frequency analysis, \emph{Proceedings of the IEEE}, \bold{84}, No. 4, 523-540. } \seealso{ \code{\link{phase.shift}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/dwpt.boot.Rd0000644000176000001440000000372312453631333015123 0ustar ripleyusers\name{dwpt.boot} \alias{dwpt.boot} \title{Bootstrap Time Series Using the DWPT} \description{ An adaptive orthonormal basis is selected in order to perform the naive bootstrap within nodes of the wavelet packet tree. A bootstrap realization of the time series is produce by applying the inverse DWPT. } \usage{dwpt.boot(y, wf, J=log(length(y),2)-1, p=1e-04, frac=1) } \arguments{ \item{y}{Not necessarily dyadic length time series.} \item{wf}{Name of the wavelet filter to use in the decomposition. See \code{\link{wave.filter}} for those wavelet filters available.} \item{J}{Depth of the discrete wavelet packet transform.} \item{p}{Level of significance for the white noise testing procedure.} \item{frac}{Fraction of the time series that should be used in constructing the likelihood function.} } \value{ Time series of length $N$, where $N$ is the length of \code{y}. } \details{ A subroutines is used to select an adaptive orthonormal basis for the piecewise-constant approximation to the underlying spectral density function (SDF). Once selected, sampling with replacement is performed within each wavelet packet coefficient vector and the new collection of wavelet packet coefficients are reconstructed into a bootstrap realization of the original time series. } \references{ Percival, D.B., S. Sardy, A. Davision (2000) Wavestrapping Time Series: Adaptive Wavelet-Based Bootstrapping, in B.J. Fitzgerald, R.L. Smith, A.T. Walden, P.C. Young (Eds.) \emph{Nonlinear and Nonstationary Signal Processing}, pp. 442-471. Whitcher, B. (2001) Simulating Gaussian Stationary Time Series with Unbounded Spectra, \emph{Journal of Computational and Graphical Statistics}, \bold{10}, No. 1, 112-134. Whitcher, B. (2004) Wavelet-Based Estimation for Seasonal Long-Memory Processes, \emph{Technometrics}, \bold{46}, No. 2, 225-238. } \seealso{ \code{\link{dwpt.sim}}, \code{\link{spp.mle}} } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/stack.plot.Rd0000644000176000001440000000215412453631333015262 0ustar ripleyusers\name{stackPlot} \alias{stackPlot} \title{Stack Plot} \description{ Stack plot of an object. This function attempts to mimic a function called \code{stack.plot} in S+WAVELETS. It is mostly a hacked version of \code{plot.ts} in \R. } \usage{stackPlot(x, plot.type = c("multiple", "single"), panel = lines, log = "", col = par("col"), bg = NA, pch = par("pch"), cex = par("cex"), lty = par("lty"), lwd = par("lwd"), ann = par("ann"), xlab = "Time", main = NULL, oma = c(6, 0, 5, 0), layout = NULL, same.scale = 1:dim(x)[2], ...) } \arguments{ \item{x}{\code{ts} object} \item{layout}{Doublet defining the dimension of the panel. If not specified, the dimensions are chosen automatically.} \item{same.scale}{Vector the same length as the number of series to be plotted. If not specified, all panels will have unique axes.} \item{plot.type,panel,log,col,bg,pch,cex,lty,lwd,ann,xlab,main,oma,...}{See \code{plot.ts}.} } %\value{} \details{ Produces a set of plots, one for each element (column) of \code{x}. } %\references{} %\seealso{} \author{Brandon Whitcher} %\examples{} \keyword{hplot} waveslim/man/nile.Rd0000644000176000001440000000177112453631333014133 0ustar ripleyusers\name{nile} \alias{nile} \title{Nile River Minima} \description{ Yearly minimal water levels of the Nile river for the years 622 to 1281, measured at the Roda gauge near Cairo (Tousson, 1925, p. 366-385). The data are listed in chronological sequence by row. The original Nile river data supplied by Beran only contained only 500 observations (622 to 1121). However, the book claimed to have 660 observations (622 to 1281). The remaining observations from the book were added, by hand, but the series still only contained 653 observations (622 to 1264). Note, now the data consists of 663 observations (spanning the years 622-1284) as in original source (Toussoun, 1925). } \usage{data(nile) } \format{A length 663 vector. } \source{ Toussoun, O. (1925) M\'emoire sur l'Histoire du Nil, Volume 18 in \emph{M\'emoires a l'Institut d'Egypte}, pp. 366-404. } \references{ Beran, J. (1994) \emph{Statistics for Long-Memory Processes}, Chapman Hall: Englewood, NJ. } \keyword{datasets} waveslim/man/japan.Rd0000644000176000001440000000104712453631333014271 0ustar ripleyusers\name{japan} \alias{japan} \title{Japanese Gross National Product} \description{ Quarterly Japanese gross national product from 1955:1 to 1996:4. } \usage{data(japan) } \format{A vector containing 169 observations. } \source{Unknown. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Hecq, A. (1998) Does seasonal adjustment induce common cycles?, \emph{Empirical Economics}, \bold{59}, 289-297. } \keyword{datasets} waveslim/man/dpss.taper.Rd0000644000176000001440000000452512453631333015267 0ustar ripleyusers\name{dpss.taper} \alias{dpss.taper} \title{Calculating Thomson's Spectral Multitapers by Inverse Iteration} \description{ The following function links the subroutines in "bell-p-w.o" to an R function in order to compute discrete prolate spheroidal sequences (dpss). } \usage{dpss.taper(n, k, nw = 4, nmax = 2^(ceiling(log(n, 2)))) } \arguments{ \item{n}{length of data taper(s)} \item{k}{number of data tapers; 1, 2, 3, ... (do not use 0!)} \item{nw}{product of length and half-bandwidth parameter (w)} \item{nmax}{maximum possible taper length, necessary for FORTRAN code} } \value{ \item{v}{matrix of data tapers (cols = tapers)} \item{eigen}{eigenvalue associated with each data taper} \item{iter}{total number of iterations performed} \item{n}{same as input} \item{w}{half-bandwidth parameter} \item{ifault}{0 indicates success, see documentation for "bell-p-w" for information on non-zero values} } \details{ Spectral estimation using a set of orthogonal tapers is becoming widely used and appreciated in scientific research. It produces direct spectral estimates with more than 2 df at each Fourier frequency, resulting in spectral estimators with reduced variance. Computation of the orthogonal tapers from the basic defining equation is difficult, however, due to the instability of the calculations -- the eigenproblem is very poorly conditioned. In this article the severe numerical instability problems are illustrated and then a technique for stable calculation of the tapers -- namely, inverse iteration -- is described. Each iteration involves the solution of a matrix equation. Because the matrix has Toeplitz form, the Levinson recursions are used to rapidly solve the matrix equation. FORTRAN code for this method is available through the Statlib archive. An alternative stable method is also briefly reviewed. } \references{ B. Bell, D. B. Percival, and A. T. Walden (1993) Calculating Thomson's spectral multitapers by inverse iteration, \emph{Journal of Computational and Graphical Statistics}, \bold{2}, No. 1, 119-130. Percival, D. B. and A. T. Walden (1993) \emph{Spectral Estimation for Physical Applications: Multitaper and Conventional Univariate Techniques}, Cambridge University Press. } \seealso{ \code{\link{sine.taper}}. } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/mult.loc.Rd0000644000176000001440000000272012453631333014734 0ustar ripleyusers\name{mult.loc} \alias{mult.loc} \title{Wavelet-based Testing and Locating for Variance Change Points} \description{ This is the major subroutine for \code{\link{testing.hov}}, providing the workhorse algorithm to recursively test and locate multiple variance changes in so-called long memory processes. } \usage{mult.loc(dwt.list, modwt.list, wf, level, min.coef, debug) } \arguments{ \item{dwt.list}{ List of wavelet vector coefficients from the \code{dwt}. } \item{modwt.list}{ List of wavelet vector coefficients from the \code{modwt}. } \item{wf}{ Name of the wavelet filter to use in the decomposition. } \item{level}{ Specifies the depth of the decomposition. } \item{min.coef}{ Minimum number of wavelet coefficients for testing purposes. } \item{debug}{ Boolean variable: if set to \code{TRUE}, actions taken by the algorithm are printed to the screen. } } \value{ Matrix. } \details{ For details see Section 9.6 of Percival and Walden (2000) or Section 7.3 in Gencay, Selcuk and Whitcher (2001). } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } \seealso{ \code{\link{rotcumvar}}, \code{\link{testing.hov}}. } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/dwpt.Rd0000644000176000001440000000545412453631333014164 0ustar ripleyusers\name{dwpt} \alias{dwpt} \alias{idwpt} \alias{modwpt} \title{(Inverse) Discrete Wavelet Packet Transforms} \description{ All possible filtering combinations (low- and high-pass) are performed to decompose a vector or time series. The resulting coefficients are associated with a binary tree structure corresponding to a partitioning of the frequency axis. } \usage{dwpt(x, wf="la8", n.levels=4, boundary="periodic") idwpt(y, y.basis) modwpt(x, wf = "la8", n.levels = 4, boundary = "periodic") } \arguments{ \item{x}{ a vector or time series containing the data be to decomposed. This must be a dyadic length vector (power of 2). } \item{wf}{ Name of the wavelet filter to use in the decomposition. By default this is set to \code{"la8"}, the Daubechies orthonormal compactly supported wavelet of length \eqn{L=8} (Daubechies, 1992), least asymmetric family. } \item{n.levels}{ Specifies the depth of the decomposition. This must be a number less than or equal to \eqn{\log(\mbox{length}(x),2)}{log2[length(x)]}. } \item{boundary}{ Character string specifying the boundary condition. If \code{boundary=="periodic"} the default, then the vector you decompose is assumed to be periodic on its defined interval,\cr if \code{boundary=="reflection"}, the vector beyond its boundaries is assumed to be a symmetric reflection of itself. } \item{y}{Object of S3 class \code{dwpt}.} \item{y.basis}{Vector of character strings that describe leaves on the DWPT basis tree.} } \value{ Basically, a list with the following components \item{w?.?}{Wavelet coefficient vectors. The first index is associated with the scale of the decomposition while the second is associated with the frequency partition within that level.} \item{wavelet}{Name of the wavelet filter used.} \item{boundary}{How the boundaries were handled.} } \details{ The code implements the one-dimensional DWPT using the pyramid algorithm (Mallat, 1989). } \references{ Mallat, S. G. (1989) A theory for multiresolution signal decomposition: the wavelet representation, \emph{IEEE Transactions on Pattern Analysis and Machine Intelligence}, \bold{11}, No. 7, 674-693. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. Wickerhauser, M. V. (1994) \emph{Adapted Wavelet Analysis from Theory to Software}, A K Peters. } \seealso{ \code{\link{dwt}}, \code{\link{modwpt}}, \code{\link{wave.filter}}. } \examples{ data(mexm) J <- 4 mexm.mra <- mra(log(mexm), "mb8", J, "modwt", "reflection") mexm.nomean <- ts( apply(matrix(unlist(mexm.mra), ncol=J+1, byrow=FALSE)[,-(J+1)], 1, sum), start=1957, freq=12) mexm.dwpt <- dwpt(mexm.nomean[-c(1:4)], "mb8", 7, "reflection") } \author{B. Whitcher} \keyword{ts} waveslim/man/wave.filter.Rd0000644000176000001440000000227712453631333015434 0ustar ripleyusers\name{wave.filter} \alias{wave.filter} \title{Select a Wavelet Filter} \description{ Converts name of wavelet filter to filter coefficients. } \usage{wave.filter(name) } \arguments{ \item{name}{Character string of wavelet filter.} } \value{ List containing the following items: \item{L}{Length of the wavelet filter.} \item{hpf}{High-pass filter coefficients.} \item{lpf}{Low-pass filter coefficients.} } \details{ Simple \code{switch} statement selects the appropriate filter. } \references{ Daubechies, I. (1992) \emph{Ten Lectures on Wavelets}, CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM: Philadelphia. Doroslovacki (1998) On the least asymmetric wavelets, \emph{IEEE Transactions for Signal Processing}, \bold{46}, No. 4, 1125-1130. Morris and Peravali (1999) Minimum-bandwidth discrete-time wavelets, \emph{Signal Processing}, \bold{76}, No. 2, 181-193. Nielsen, M. (2000) On the Construction and Frequency Localization of Orthogonal Quadrature Filters, \emph{Journal of Approximation Theory}, \bold{108}, No. 1, 36-52. } \seealso{ \code{\link{wavelet.filter}}, \code{\link{squared.gain}}. } %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/brick.wall.Rd0000644000176000001440000000260712453631333015233 0ustar ripleyusers\name{brick.wall} \alias{brick.wall} \alias{dwpt.brick.wall} \title{Replace Boundary Wavelet Coefficients with Missing Values} \description{ Sets the first \eqn{n} wavelet coefficients to \code{NA}. } \usage{brick.wall(x, wf, method="modwt") dwpt.brick.wall(x, wf, n.levels, method="modwpt") } \arguments{ \item{x}{DWT/MODWT/DWPT/MODWPT object} \item{wf}{Character string; name of wavelet filter} \item{method}{Either \code{\link{dwt}} or \code{\link{modwt}} for \code{brick.wall}, or either \code{\link{dwpt}} or \code{\link{modwpt}} for \code{dwpt.brick.wall}} \item{n.levels}{depth of the wavelet transform} } \value{ Same object as \code{x} only with some missing values. } \details{ The fact that observed time series are finite causes boundary issues. One way to get around this is to simply remove any wavelet coefficient computed involving the boundary. This is done here by replacing boundary wavelet coefficients with \code{NA}. } \references{ Lindsay, R. W., D. B. Percival and D. A. Rothrock (1996). The discrete wavelet transform and the scale anlaysis of the surface properties of sea ice, \emph{IEEE Transactions on Geoscience and Remote Sensing}, \bold{34}, No.~3, 771-787. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. } %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/barbara.Rd0000644000176000001440000000044712453631333014575 0ustar ripleyusers\name{barbara} \alias{barbara} \title{Barbara Test Image} \description{ The Barbara image comes from Allen Gersho's lab at the University of California, Santa Barbara. } \usage{data(barbara) } \format{A 256 \eqn{\times}{x} 256 matrix. } \source{Internet. } %\references{} \keyword{datasets} waveslim/man/wave.variance.Rd0000644000176000001440000000725412453631333015737 0ustar ripleyusers\name{wave.variance} \alias{wave.variance} \alias{wave.covariance} \alias{wave.correlation} \title{Wavelet Analysis of Univariate/Bivariate Time Series} \description{ Produces an estimate of the multiscale variance, covariance or correlation along with approximate confidence intervals. } \usage{wave.variance(x, type="eta3", p=0.025) wave.covariance(x, y) wave.correlation(x, y, N, p=0.975) } \arguments{ \item{x}{first time series} \item{y}{second time series} \item{type}{character string describing confidence interval calculation; valid methods are \code{gaussian}, \code{eta1}, \code{eta2}, \code{eta3}, \code{nongaussian}} \item{p}{(one minus the) two-sided p-value for the confidence interval} \item{N}{length of time series} } \value{ Matrix with as many rows as levels in the wavelet transform object. The first column provides the point estimate for the wavelet variance, covariance, or correlation followed by the lower and upper bounds from the confidence interval. } \details{ The time-independent wavelet variance is basically the average of the squared wavelet coefficients across each scale. As shown in Percival (1995), the wavelet variance is a scale-by-scale decomposition of the variance for a stationary process, and certain non-stationary processes. } \references{ Gencay, R., F. Selcuk and B. Whitcher (2001) \emph{An Introduction to Wavelets and Other Filtering Methods in Finance and Economics}, Academic Press. Percival, D. B. (1995) \emph{Biometrika}, \bold{82}, No. 3, 619-631. Percival, D. B. and A. T. Walden (2000) \emph{Wavelet Methods for Time Series Analysis}, Cambridge University Press. Whitcher, B., P. Guttorp and D. B. Percival (2000) Wavelet Analysis of Covariance with Application to Atmospheric Time Series, \emph{Journal of Geophysical Research}, \bold{105}, No. D11, 14,941-14,962. } %\seealso{} \examples{ ## Figure 7.3 from Gencay, Selcuk and Whitcher (2001) data(ar1) ar1.modwt <- modwt(ar1, "haar", 6) ar1.modwt.bw <- brick.wall(ar1.modwt, "haar") ar1.modwt.var2 <- wave.variance(ar1.modwt.bw, type="gaussian") ar1.modwt.var <- wave.variance(ar1.modwt.bw, type="nongaussian") par(mfrow=c(1,1), las=1, mar=c(5,4,4,2)+.1) matplot(2^(0:5), ar1.modwt.var2[-7,], type="b", log="xy", xaxt="n", ylim=c(.025, 6), pch="*LU", lty=1, col=c(1,4,4), xlab="Wavelet Scale", ylab="") matlines(2^(0:5), as.matrix(ar1.modwt.var)[-7,2:3], type="b", pch="LU", lty=1, col=3) axis(side=1, at=2^(0:5)) legend(1, 6, c("Wavelet variance", "Gaussian CI", "Non-Gaussian CI"), lty=1, col=c(1,4,3), bty="n") ## Figure 7.8 from Gencay, Selcuk and Whitcher (2001) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) wf <- "d4" J <- 6 demusd.modwt <- modwt(returns[,"DEM.USD"], wf, J) demusd.modwt.bw <- brick.wall(demusd.modwt, wf) jpyusd.modwt <- modwt(returns[,"JPY.USD"], wf, J) jpyusd.modwt.bw <- brick.wall(jpyusd.modwt, wf) returns.modwt.cov <- wave.covariance(demusd.modwt.bw, jpyusd.modwt.bw) par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) matplot(2^(0:(J-1)), returns.modwt.cov[-(J+1),], type="b", log="x", pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", ylab="Wavelet Covariance") axis(side=1, at=2^(0:7)) abline(h=0) returns.modwt.cor <- wave.correlation(demusd.modwt.bw, jpyusd.modwt.bw, N = dim(returns)[1]) par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) matplot(2^(0:(J-1)), returns.modwt.cor[-(J+1),], type="b", log="x", pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", ylab="Wavelet Correlation") axis(side=1, at=2^(0:7)) abline(h=0) } \author{B. Whitcher} \keyword{ts} waveslim/man/denoise.dwt.2d.Rd0000644000176000001440000000460512453631333015732 0ustar ripleyusers\name{denoise.2d} \alias{denoise.dwt.2d} \alias{denoise.modwt.2d} \title{Denoise an Image via the 2D Discrete Wavelet Transform} \description{ Perform simple de-noising of an image using the two-dimensional discrete wavelet transform. } \usage{ denoise.dwt.2d(x, wf = "la8", J = 4, method = "universal", H = 0.5, noise.dir = 3, rule = "hard") denoise.modwt.2d(x, wf = "la8", J = 4, method = "universal", H = 0.5, rule = "hard") } \arguments{ \item{x}{input matrix (image)} \item{wf}{name of the wavelet filter to use in the decomposition} \item{J}{depth of the decomposition, must be a number less than or equal to \eqn{\log_2(\min\{M,N\})}{log(min{M,N},2)}} \item{method}{character string describing the threshold applied, only \code{"universal"} and \code{"long-memory"} are currently implemented} \item{H}{self-similarity or Hurst parameter to indicate spectral scaling, white noise is 0.5} \item{noise.dir}{number of directions to estimate background noise standard deviation, the default is 3 which produces a unique estimate of the background noise for each spatial direction} \item{rule}{either a \code{"hard"} or \code{"soft"} thresholding rule may be used} } \value{ Image of the same dimension as the original but with high-freqency fluctuations removed. } \details{ See \code{\link{Thresholding}}. } \references{ See \code{\link{Thresholding}} for references concerning de-noising in one dimension. } \seealso{\code{\link{Thresholding}}} \examples{ ## Xbox image data(xbox) n <- NROW(xbox) xbox.noise <- xbox + matrix(rnorm(n*n, sd=.15), n, n) par(mfrow=c(2,2), cex=.8, pty="s") image(xbox.noise, col=rainbow(128), main="Original Image") image(denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128), zlim=range(xbox.noise), main="Denoised image") image(xbox.noise - denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128), zlim=range(xbox.noise), main="Residual image") ## Daubechies image data(dau) n <- NROW(dau) dau.noise <- dau + matrix(rnorm(n*n, sd=10), n, n) par(mfrow=c(2,2), cex=.8, pty="s") image(dau.noise, col=rainbow(128), main="Original Image") dau.denoise <- denoise.modwt.2d(dau.noise, wf="d4", rule="soft") image(dau.denoise, col=rainbow(128), zlim=range(dau.noise), main="Denoised image") image(dau.noise - dau.denoise, col=rainbow(128), main="Residual image") } \author{B. Whitcher} \keyword{ts} waveslim/man/cplxdual.Rd0000644000176000001440000000277312453631333015023 0ustar ripleyusers\name{Dualtree Complex} \alias{cplxdual2D} \alias{icplxdual2D} \title{Dual-tree Complex 2D Discrete Wavelet Transform} \description{ Dual-tree complex 2D discrete wavelet transform (DWT). } \usage{ cplxdual2D(x, J, Faf, af) icplxdual2D(w, J, Fsf, sf) } \arguments{ \item{x}{2D array.} \item{w}{wavelet coefficients.} \item{J}{number of stages.} \item{Faf}{first stage analysis filters for tree \eqn{i}.} \item{af}{analysis filters for the remaining stages on tree \eqn{i}.} \item{Fsf}{last stage synthesis filters for tree \eqn{i}.} \item{sf}{synthesis filters for the preceeding stages.} } %\details{} \value{ For the analysis of \code{x}, the output is \item{w}{wavelet coefficients indexed by \code{[[j]][[i]][[d1]][[d2]]}, where \eqn{j=1,\ldots,J} (scale), \eqn{i=1} (real part) or \eqn{i=2} (imag part), \eqn{d1=1,2} and \eqn{d2=1,2,3} (orientations).} For the synthesis of \code{w}, the output is \item{y}{output signal.} } \references{ WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY\cr \url{http://taco.poly.edu/WaveletSoftware/} } \seealso{ \code{\link{FSfarras}}, \code{\link{farras}}, \code{\link{afb2D}}, \code{\link{sfb2D}}. } \examples{ \dontrun{ ## EXAMPLE: cplxdual2D x = matrix(rnorm(32*32), 32, 32) J = 5 Faf = FSfarras()$af Fsf = FSfarras()$sf af = dualfilt1()$af sf = dualfilt1()$sf w = cplxdual2D(x, J, Faf, af) y = icplxdual2D(w, J, Fsf, sf) err = x - y max(abs(err)) } } \author{Matlab: S. Cai, K. Li and I. Selesnick; R port: B. Whitcher} \keyword{ts} waveslim/man/doppler.Rd0000644000176000001440000000072312453631333014645 0ustar ripleyusers\name{doppler} \alias{doppler} \title{Sinusoid with Changing Amplitude and Frequency} \description{ \deqn{doppler(x) = \sqrt{x(1 - x)} \sin\left(\frac{2.1\pi}{x+0.05}\right)}{% doppler(x) = sqrt{x(1-x)} sin[(2.1*pi)/(x+0.05)]} } \usage{data(doppler) } \format{A vector containing 512 observations. } \source{S+WAVELETS. } \references{ Bruce, A., and H.-Y. Gao (1996) \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. } \keyword{datasets} waveslim/man/linchirp.Rd0000644000176000001440000000060112453631333015003 0ustar ripleyusers\name{linchirp} \alias{linchirp} \title{Linear Chirp} \description{ \deqn{linchirp(x) = \sin(0.125 \pi n x^2)}{% linchirp(x) = sin(0.125*pi*n*x^2)} } \usage{data(linchirp) } \format{A vector containing 512 observations. } \source{S+WAVELETS. } \references{ Bruce, A., and H.-Y. Gao (1996) \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. } \keyword{datasets} waveslim/man/Dualtree.Rd0000644000176000001440000000504012453631333014742 0ustar ripleyusers\name{Dualtree} \alias{dualtree} \alias{idualtree} \alias{dualtree2D} \alias{idualtree2D} \title{Dual-tree Complex Discrete Wavelet Transform} \description{ One- and two-dimensional dual-tree complex discrete wavelet transforms developed by Kingsbury and Selesnick \emph{et al.} } \usage{ dualtree(x, J, Faf, af) idualtree(w, J, Fsf, sf) dualtree2D(x, J, Faf, af) idualtree2D(w, J, Fsf, sf) } \arguments{ \item{x}{\eqn{N}-point vector or \eqn{M{\times}N}{MxN} matrix.} \item{w}{DWT coefficients.} \item{J}{number of stages.} \item{Faf}{analysis filters for the first stage.} \item{af}{analysis filters for the remaining stages.} \item{Fsf}{synthesis filters for the last stage.} \item{sf}{synthesis filters for the preceeding stages.} } \value{ For the analysis of \code{x}, the output is \item{w}{DWT coefficients. Each wavelet scale is a list containing the real and imaginary parts. The final scale (\eqn{J+1}) contains the low-pass filter coefficients.} For the synthesis of \code{w}, the output is \item{y}{output signal} } \details{ In one dimension \eqn{N} is divisible by \eqn{2^J} and \eqn{N\ge2^{J-1}\cdot\mbox{length}(\mbox{\code{af}})}. In two dimensions, these two conditions must hold for both \eqn{M} and \eqn{N}. } \references{ WAVELET SOFTWARE AT POLYTECHNIC UNIVERSITY, BROOKLYN, NY\cr \url{http://taco.poly.edu/WaveletSoftware/} } \seealso{ \code{\link{FSfarras}}, \code{\link{farras}}, \code{\link{convolve}}, \code{\link{cshift}}, \code{\link{afb}}, \code{\link{sfb}}. } \examples{ ## EXAMPLE: dualtree x = rnorm(512) J = 4 Faf = FSfarras()$af Fsf = FSfarras()$sf af = dualfilt1()$af sf = dualfilt1()$sf w = dualtree(x, J, Faf, af) y = idualtree(w, J, Fsf, sf) err = x - y max(abs(err)) ## Example: dualtree2D x = matrix(rnorm(64*64), 64, 64) J = 3 Faf = FSfarras()$af Fsf = FSfarras()$sf af = dualfilt1()$af sf = dualfilt1()$sf w = dualtree2D(x, J, Faf, af) y = idualtree2D(w, J, Fsf, sf) err = x - y max(abs(err)) ## Display 2D wavelets of dualtree2D.m J <- 4 L <- 3 * 2^(J+1) N <- L / 2^J Faf <- FSfarras()$af Fsf <- FSfarras()$sf af <- dualfilt1()$af sf <- dualfilt1()$sf x <- matrix(0, 2*L, 3*L) w <- dualtree2D(x, J, Faf, af) w[[J]][[1]][[1]][N/2, N/2+0*N] <- 1 w[[J]][[1]][[2]][N/2, N/2+1*N] <- 1 w[[J]][[1]][[3]][N/2, N/2+2*N] <- 1 w[[J]][[2]][[1]][N/2+N, N/2+0*N] <- 1 w[[J]][[2]][[2]][N/2+N, N/2+1*N] <- 1 w[[J]][[2]][[3]][N/2+N, N/2+2*N] <- 1 y <- idualtree2D(w, J, Fsf, sf) image(t(y), col=grey(0:64/64), axes=FALSE) } \author{Matlab: S. Cai, K. Li and I. Selesnick; R port: B. Whitcher} \keyword{ts} waveslim/man/spp.var.Rd0000644000176000001440000000175312453631333014575 0ustar ripleyusers\name{spp.var} \alias{spp.var} \alias{Hypergeometric} \title{Variance of a Seasonal Persistent Process} \description{ Computes the variance of a seasonal persistent (SP) process using a hypergeometric series expansion. } \usage{ spp.var(d, fG, sigma2 = 1) Hypergeometric(a, b, c, z) } \arguments{ \item{d}{Fractional difference parameter.} \item{fG}{Gegenbauer frequency.} \item{sigma2}{Innovations variance.} \item{a,b,c,z}{Parameters for the hypergeometric series.} } \value{ The variance of an SP process. } \details{ See Lapsa (1997). The subroutine to compute a hypergeometric series was taken from \emph{Numerical Recipes in C}. } \references{ Lapsa, P.M. (1997) Determination of Gegenbauer-type random process models. \emph{Signal Processing} \bold{63}, 73-90. Press, W.H., S.A. Teukolsky, W.T. Vetterling and B.P. Flannery (1992) \emph{Numerical Recipes in C}, 2nd edition, Cambridge University Press. } %\seealso{} %\examples{} \author{B. Whitcher} \keyword{ts} waveslim/man/xbox.Rd0000644000176000001440000000101112453631333014147 0ustar ripleyusers\name{xbox} \alias{xbox} \title{Image with Box and X} \description{ \deqn{xbox(i,j) = I_{[i=n/4,\;3n/4,\;j;~ n/4 \leq j \leq 3n/4]} + I_{[n/4 \leq i \leq 3n/4;~ j=n/4,\;3n/4,\;i]}}{% xbox(i,j) = I_[i = n/4, 3n/4, j; n/4 \leq j \leq 3n/4] + I_[n/4 \leq i \leq 3n/4; j = n/4, 3n/4, i]} } \usage{data(xbox) } \format{A 128 \eqn{\times}{x} 128 matrix. } \source{S+WAVELETS. } \references{ Bruce, A., and H.-Y. Gao (1996) \emph{Applied Wavelet Analysis with S-PLUS}, Springer: New York. } \keyword{datasets} waveslim/DESCRIPTION0000644000176000001440000000227413622230602013640 0ustar ripleyusersPackage: waveslim Version: 1.7.5.2 Date: 2014-12-21 Title: Basic Wavelet Routines for One-, Two- And Three-Dimensional Signal Processing Author: Brandon Whitcher Maintainer: ORPHANED Depends: R (>= 2.11.0), graphics, grDevices, stats, utils Suggests: fftw Description: Basic wavelet routines for time series (1D), image (2D) and array (3D) analysis. The code provided here is based on wavelet methodology developed in Percival and Walden (2000); Gencay, Selcuk and Whitcher (2001); the dual-tree complex wavelet transform (DTCWT) from Kingsbury (1999, 2001) as implemented by Selesnick; and Hilbert wavelet pairs (Selesnick 2001, 2002). All figures in chapters 4-7 of GSW (2001) are reproducible using this package and R code available at the book website(s) below. License: BSD_3_clause + file LICENSE URL: http://waveslim.blogspot.com, http://www2.imperial.ac.uk/~bwhitche/book NeedsCompilation: yes Packaged: 2020-02-16 12:06:44 UTC; ripley Repository: CRAN Date/Publication: 2020-02-16 12:11:46 UTC X-CRAN-Original-Maintainer: Brandon Whitcher X-CRAN-Comment: Orphaned and corrected on 2020-02-16 as there was no response to repeated requests. waveslim/tests/0000755000176000001440000000000012453631330013273 5ustar ripleyuserswaveslim/tests/Examples/0000755000176000001440000000000013622226442015054 5ustar ripleyuserswaveslim/tests/Examples/waveslim-Ex.Rout.save0000644000176000001440000007747513622230060021100 0ustar ripleyusers R Under development (unstable) (2020-02-16 r77809) -- "Unsuffered Consequences" Copyright (C) 2020 The R Foundation for Statistical Computing Platform: x86_64-pc-linux-gnu (64-bit) R is free software and comes with ABSOLUTELY NO WARRANTY. You are welcome to redistribute it under certain conditions. Type 'license()' or 'licence()' for distribution details. Natural language support but running in an English locale R is a collaborative project with many contributors. Type 'contributors()' for more information and 'citation()' on how to cite R or R packages in publications. Type 'demo()' for some demos, 'help()' for on-line help, or 'help.start()' for an HTML browser interface to help. Type 'q()' to quit R. > pkgname <- "waveslim" > source(file.path(R.home("share"), "R", "examples-header.R")) > options(warn = 1) > library('waveslim') waveslim: Wavelet Method for 1/2/3D Signals (version = 1.7.5.2) > > base::assign(".oldSearch", base::search(), pos = 'CheckExEnv') > base::assign(".old_wd", base::getwd(), pos = 'CheckExEnv') > cleanEx() > nameEx("Dualtree") > ### * Dualtree > > flush(stderr()); flush(stdout()) > > ### Name: Dualtree > ### Title: Dual-tree Complex Discrete Wavelet Transform > ### Aliases: dualtree idualtree dualtree2D idualtree2D > ### Keywords: ts > > ### ** Examples > > ## EXAMPLE: dualtree > x = rnorm(512) > J = 4 > Faf = FSfarras()$af > Fsf = FSfarras()$sf > af = dualfilt1()$af > sf = dualfilt1()$sf > w = dualtree(x, J, Faf, af) > y = idualtree(w, J, Fsf, sf) > err = x - y > max(abs(err)) [1] 1.688595e-08 > > ## Example: dualtree2D > x = matrix(rnorm(64*64), 64, 64) > J = 3 > Faf = FSfarras()$af > Fsf = FSfarras()$sf > af = dualfilt1()$af > sf = dualfilt1()$sf > w = dualtree2D(x, J, Faf, af) > y = idualtree2D(w, J, Fsf, sf) > err = x - y > max(abs(err)) [1] 2.385238e-08 > > ## Display 2D wavelets of dualtree2D.m > > J <- 4 > L <- 3 * 2^(J+1) > N <- L / 2^J > Faf <- FSfarras()$af > Fsf <- FSfarras()$sf > af <- dualfilt1()$af > sf <- dualfilt1()$sf > x <- matrix(0, 2*L, 3*L) > w <- dualtree2D(x, J, Faf, af) > w[[J]][[1]][[1]][N/2, N/2+0*N] <- 1 > w[[J]][[1]][[2]][N/2, N/2+1*N] <- 1 > w[[J]][[1]][[3]][N/2, N/2+2*N] <- 1 > w[[J]][[2]][[1]][N/2+N, N/2+0*N] <- 1 > w[[J]][[2]][[2]][N/2+N, N/2+1*N] <- 1 > w[[J]][[2]][[3]][N/2+N, N/2+2*N] <- 1 > y <- idualtree2D(w, J, Fsf, sf) > image(t(y), col=grey(0:64/64), axes=FALSE) > > > > cleanEx() > nameEx("basis") > ### * basis > > flush(stderr()); flush(stdout()) > > ### Name: basis > ### Title: Produce Boolean Vector from Wavelet Basis Names > ### Aliases: basis > ### Keywords: ts > > ### ** Examples > > data(acvs.andel8) > ## Not run: > ##D x <- hosking.sim(1024, acvs.andel8[,2]) > ##D x.dwpt <- dwpt(x, "la8", 7) > ##D ## Select orthonormal basis from wavelet packet tree > ##D x.basis <- basis(x.dwpt, c("w1.1","w2.1","w3.0","w4.3","w5.4","w6.10", > ##D "w7.22","w7.23")) > ##D for(i in 1:length(x.dwpt)) > ##D x.dwpt[[i]] <- x.basis[i] * x.dwpt[[i]] > ##D ## Resonstruct original series using selected orthonormal basis > ##D y <- idwpt(x.dwpt, x.basis) > ##D par(mfrow=c(2,1), mar=c(5-1,4,4-1,2)) > ##D plot.ts(x, xlab="", ylab="", main="Original Series") > ##D plot.ts(y, xlab="", ylab="", main="Reconstructed Series") > ## End(Not run) > > > > cleanEx() > nameEx("cplxdual") > ### * cplxdual > > flush(stderr()); flush(stdout()) > > ### Name: Dualtree Complex > ### Title: Dual-tree Complex 2D Discrete Wavelet Transform > ### Aliases: cplxdual2D icplxdual2D > ### Keywords: ts > > ### ** Examples > > ## Not run: > ##D ## EXAMPLE: cplxdual2D > ##D x = matrix(rnorm(32*32), 32, 32) > ##D J = 5 > ##D Faf = FSfarras()$af > ##D Fsf = FSfarras()$sf > ##D af = dualfilt1()$af > ##D sf = dualfilt1()$sf > ##D w = cplxdual2D(x, J, Faf, af) > ##D y = icplxdual2D(w, J, Fsf, sf) > ##D err = x - y > ##D max(abs(err)) > ## End(Not run) > > > > cleanEx() > nameEx("denoise.dwt.2d") > ### * denoise.dwt.2d > > flush(stderr()); flush(stdout()) > > ### Name: denoise.2d > ### Title: Denoise an Image via the 2D Discrete Wavelet Transform > ### Aliases: denoise.dwt.2d denoise.modwt.2d > ### Keywords: ts > > ### ** Examples > > ## Xbox image > data(xbox) > n <- NROW(xbox) > xbox.noise <- xbox + matrix(rnorm(n*n, sd=.15), n, n) > par(mfrow=c(2,2), cex=.8, pty="s") > image(xbox.noise, col=rainbow(128), main="Original Image") > image(denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128), + zlim=range(xbox.noise), main="Denoised image") > image(xbox.noise - denoise.dwt.2d(xbox.noise, wf="haar"), col=rainbow(128), + zlim=range(xbox.noise), main="Residual image") > > ## Daubechies image > data(dau) > n <- NROW(dau) > dau.noise <- dau + matrix(rnorm(n*n, sd=10), n, n) > par(mfrow=c(2,2), cex=.8, pty="s") > image(dau.noise, col=rainbow(128), main="Original Image") > dau.denoise <- denoise.modwt.2d(dau.noise, wf="d4", rule="soft") > image(dau.denoise, col=rainbow(128), zlim=range(dau.noise), + main="Denoised image") > image(dau.noise - dau.denoise, col=rainbow(128), main="Residual image") > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("dwpt") > ### * dwpt > > flush(stderr()); flush(stdout()) > > ### Name: dwpt > ### Title: (Inverse) Discrete Wavelet Packet Transforms > ### Aliases: dwpt idwpt modwpt > ### Keywords: ts > > ### ** Examples > > data(mexm) > J <- 4 > mexm.mra <- mra(log(mexm), "mb8", J, "modwt", "reflection") > mexm.nomean <- ts( + apply(matrix(unlist(mexm.mra), ncol=J+1, byrow=FALSE)[,-(J+1)], 1, sum), + start=1957, freq=12) > mexm.dwpt <- dwpt(mexm.nomean[-c(1:4)], "mb8", 7, "reflection") > > > > cleanEx() > nameEx("dwpt.sim") > ### * dwpt.sim > > flush(stderr()); flush(stdout()) > > ### Name: dwpt.sim > ### Title: Simulate Seasonal Persistent Processes Using the DWPT > ### Aliases: dwpt.sim > ### Keywords: ts > > ### ** Examples > > ## Generate monthly time series with annual oscillation > ## library(ts) is required in order to access acf() > x <- dwpt.sim(256, "mb16", .4, 1/12, M=4, epsilon=.001) > par(mfrow=c(2,1)) > plot(x, type="l", xlab="Time") > acf(x, lag.max=128, ylim=c(-.6,1)) > data(acvs.andel8) > lines(acvs.andel8$lag[1:128], acvs.andel8$acf[1:128], col=2) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("dwt.2d") > ### * dwt.2d > > flush(stderr()); flush(stdout()) > > ### Name: dwt.2d > ### Title: Two-Dimensional Discrete Wavelet Transform > ### Aliases: dwt.2d idwt.2d > ### Keywords: ts > > ### ** Examples > > ## Xbox image > data(xbox) > xbox.dwt <- dwt.2d(xbox, "haar", 3) > par(mfrow=c(1,1), pty="s") > plot.dwt.2d(xbox.dwt) > par(mfrow=c(2,2), pty="s") > image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox, xlab="", ylab="", + main="Original Image") > image(1:dim(xbox)[1], 1:dim(xbox)[2], idwt.2d(xbox.dwt), xlab="", ylab="", + main="Wavelet Reconstruction") > image(1:dim(xbox)[1], 1:dim(xbox)[2], xbox - idwt.2d(xbox.dwt), + xlab="", ylab="", main="Difference") > > ## Daubechies image > data(dau) > par(mfrow=c(1,1), pty="s") > image(dau, col=rainbow(128)) > sum(dau^2) [1] 1049732962 > dau.dwt <- dwt.2d(dau, "d4", 3) > plot.dwt.2d(dau.dwt) > sum(plot.dwt.2d(dau.dwt, plot=FALSE)^2) [1] 1049732962 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("dwt") > ### * dwt > > flush(stderr()); flush(stdout()) > > ### Name: dwt > ### Title: Discrete Wavelet Transform (DWT) > ### Aliases: dwt dwt.nondyadic idwt > ### Keywords: ts > > ### ** Examples > > ## Figures 4.17 and 4.18 in Gencay, Selcuk and Whitcher (2001). > data(ibm) > ibm.returns <- diff(log(ibm)) > ## Haar > ibmr.haar <- dwt(ibm.returns, "haar") > names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4") > ## plot partial Haar DWT for IBM data > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)") > for(i in 1:4) + plot.ts(up.sample(ibmr.haar[[i]], 2^i), type="h", axes=FALSE, + ylab=names(ibmr.haar)[i]) > plot.ts(up.sample(ibmr.haar$v4, 2^4), type="h", axes=FALSE, + ylab=names(ibmr.haar)[5]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > ## LA(8) > ibmr.la8 <- dwt(ibm.returns, "la8") > names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4") > ## must shift LA(8) coefficients > ibmr.la8$w1 <- c(ibmr.la8$w1[-c(1:2)], ibmr.la8$w1[1:2]) > ibmr.la8$w2 <- c(ibmr.la8$w2[-c(1:2)], ibmr.la8$w2[1:2]) > for(i in names(ibmr.la8)[3:4]) + ibmr.la8[[i]] <- c(ibmr.la8[[i]][-c(1:3)], ibmr.la8[[i]][1:3]) > ibmr.la8$v4 <- c(ibmr.la8$v4[-c(1:2)], ibmr.la8$v4[1:2]) > ## plot partial LA(8) DWT for IBM data > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)") > for(i in 1:4) + plot.ts(up.sample(ibmr.la8[[i]], 2^i), type="h", axes=FALSE, + ylab=names(ibmr.la8)[i]) > plot.ts(up.sample(ibmr.la8$v4, 2^4), type="h", axes=FALSE, + ylab=names(ibmr.la8)[5]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("fb") > ### * fb > > flush(stderr()); flush(stdout()) > > ### Name: Dual-tree Filter Banks > ### Title: Filter Banks for Dual-Tree Wavelet Transforms > ### Aliases: afb afb2D afb2D.A sfb sfb2D sfb2D.A > ### Keywords: ts > > ### ** Examples > > ## EXAMPLE: afb, sfb > af = farras()$af > sf = farras()$sf > x = rnorm(64) > x.afb = afb(x, af) > lo = x.afb$lo > hi = x.afb$hi > y = sfb(lo, hi, sf) > err = x - y > max(abs(err)) [1] 2.337019e-14 > > ## EXAMPLE: afb2D, sfb2D > x = matrix(rnorm(32*64), 32, 64) > af = farras()$af > sf = farras()$sf > x.afb2D = afb2D(x, af, af) > lo = x.afb2D$lo > hi = x.afb2D$hi > y = sfb2D(lo, hi, sf, sf) > err = x - y > max(abs(err)) [1] 5.839773e-14 > > ## Example: afb2D.A, sfb2D.A > x = matrix(rnorm(32*64), 32, 64) > af = farras()$af > sf = farras()$sf > x.afb2D.A = afb2D.A(x, af, 1) > lo = x.afb2D.A$lo > hi = x.afb2D.A$hi > y = sfb2D.A(lo, hi, sf, 1) > err = x - y > max(abs(err)) [1] 4.156397e-14 > > > > cleanEx() > nameEx("fdp.mle") > ### * fdp.mle > > flush(stderr()); flush(stdout()) > > ### Name: fdp.mle > ### Title: Wavelet-based Maximum Likelihood Estimation for a Fractional > ### Difference Process > ### Aliases: fdp.mle > ### Keywords: ts > > ### ** Examples > > ## Figure 5.5 in Gencay, Selcuk and Whitcher (2001) > fdp.sdf <- function(freq, d, sigma2=1) + sigma2 / ((2*sin(pi * freq))^2)^d > dB <- function(x) 10 * log10(x) > per <- function(z) { + n <- length(z) + (Mod(fft(z))**2/(2*pi*n))[1:(n %/% 2 + 1)] + } > data(ibm) > ibm.returns <- diff(log(ibm)) > ibm.volatility <- abs(ibm.returns) > ibm.vol.mle <- fdp.mle(ibm.volatility, "d4", 4) > freq <- 0:184/368 > ibm.vol.per <- 2 * pi * per(ibm.volatility) > ibm.vol.resid <- ibm.vol.per/ fdp.sdf(freq, ibm.vol.mle$parameters[1]) > par(mfrow=c(1,1), las=0, pty="m") > plot(freq, dB(ibm.vol.per), type="l", xlab="Frequency", ylab="Spectrum") > lines(freq, dB(fdp.sdf(freq, ibm.vol.mle$parameters[1], + ibm.vol.mle$parameters[2]/2)), col=2) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("hilbert.filter") > ### * hilbert.filter > > flush(stderr()); flush(stdout()) > > ### Name: hilbert.filter > ### Title: Select a Hilbert Wavelet Pair > ### Aliases: hilbert.filter > ### Keywords: ts > > ### ** Examples > > hilbert.filter("k3l3") $length [1] 12 $hpf $hpf[[1]] [1] -0.0022260892 0.0426791770 0.0248291600 -0.4982782400 0.7997265200 [6] -0.2867863600 -0.1564275500 0.0331898960 0.0434276420 0.0022046914 [11] -0.0022229002 -0.0001159435 $hpf[[2]] [1] -1.558262e-02 4.943225e-02 2.167541e-01 -7.458501e-01 6.133371e-01 [6] 1.550640e-02 -1.270504e-01 -3.236969e-02 1.970114e-02 6.190912e-03 [11] -5.254341e-05 -1.656336e-05 $lpf $lpf[[1]] [1] 0.0001159435 -0.0022229002 -0.0022046914 0.0434276420 -0.0331898960 [6] -0.1564275500 0.2867863600 0.7997265200 0.4982782400 0.0248291600 [11] -0.0426791770 -0.0022260892 $lpf[[2]] [1] 1.656336e-05 -5.254341e-05 -6.190912e-03 1.970114e-02 3.236969e-02 [6] -1.270504e-01 -1.550640e-02 6.133371e-01 7.458501e-01 2.167541e-01 [11] -4.943225e-02 -1.558262e-02 > hilbert.filter("k3l5") $length [1] 12 $hpf $hpf[[1]] [1] -5.854176e-06 2.299268e-04 2.864101e-03 -1.273398e-02 -5.957379e-02 [6] 1.300891e-01 2.653746e-01 -7.875716e-01 5.340248e-01 -3.981034e-03 [11] -4.557677e-02 -3.574788e-02 1.021288e-02 2.614091e-03 -2.131052e-04 [16] -5.425879e-06 $hpf[[2]] [1] -6.439594e-05 -4.664223e-05 9.547891e-03 6.282690e-03 -1.233684e-01 [6] 4.621801e-03 5.832856e-01 -7.650914e-01 2.292948e-01 7.456225e-02 [11] 9.250975e-03 -2.860147e-02 -8.400312e-04 1.166470e-03 3.572714e-07 [16] -4.932617e-07 $lpf $lpf[[1]] [1] 5.425879e-06 -2.131052e-04 -2.614091e-03 1.021288e-02 3.574788e-02 [6] -4.557677e-02 3.981034e-03 5.340248e-01 7.875716e-01 2.653746e-01 [11] -1.300891e-01 -5.957379e-02 1.273398e-02 2.864101e-03 -2.299268e-04 [16] -5.854176e-06 $lpf[[2]] [1] 4.932617e-07 3.572714e-07 -1.166470e-03 -8.400312e-04 2.860147e-02 [6] 9.250975e-03 -7.456225e-02 2.292948e-01 7.650914e-01 5.832856e-01 [11] -4.621801e-03 -1.233684e-01 -6.282690e-03 9.547891e-03 4.664223e-05 [16] -6.439594e-05 > hilbert.filter("k4l2") $length [1] 12 $hpf $hpf[[1]] [1] 0.002285229 -0.017099408 -0.061694251 0.160409270 0.227520750 [6] -0.774586170 0.560358370 -0.041525062 -0.034722190 -0.036090743 [11] 0.013358873 0.001785330 $hpf[[2]] [1] 0.0114261460 0.0059121296 -0.1332013800 0.0403150080 0.5409737900 [6] -0.7795662200 0.2746430800 0.0584667250 0.0134499020 -0.0325914860 [11] -0.0001847535 0.0003570660 $lpf $lpf[[1]] [1] -0.001785330 0.013358873 0.036090743 -0.034722190 0.041525062 [6] 0.560358370 0.774586170 0.227520750 -0.160409270 -0.061694251 [11] 0.017099408 0.002285229 $lpf[[2]] [1] -0.0003570660 -0.0001847535 0.0325914860 0.0134499020 -0.0584667250 [6] 0.2746430800 0.7795662200 0.5409737900 -0.0403150080 -0.1332013800 [11] -0.0059121296 0.0114261460 > hilbert.filter("k4l4") $length [1] 16 $hpf $hpf[[1]] [1] -2.593319e-05 6.742522e-04 5.732357e-03 -1.697939e-02 -6.975951e-02 [6] 1.337267e-01 2.790955e-01 -7.833091e-01 5.302173e-01 -8.136445e-03 [11] -5.068726e-02 -3.860533e-02 1.320347e-02 5.548244e-03 -6.690907e-04 [16] -2.573467e-05 $hpf[[2]] [1] -2.333987e-04 -1.556956e-04 1.548964e-02 9.196125e-03 -1.352010e-01 [6] -5.170879e-03 5.883470e-01 -7.574938e-01 2.329811e-01 7.708457e-02 [11] 7.702384e-03 -3.355466e-02 -1.980900e-03 2.990384e-03 1.907454e-06 [16] -2.859407e-06 $lpf $lpf[[1]] [1] 2.573467e-05 -6.690907e-04 -5.548244e-03 1.320347e-02 3.860533e-02 [6] -5.068726e-02 8.136445e-03 5.302173e-01 7.833091e-01 2.790955e-01 [11] -1.337267e-01 -6.975951e-02 1.697939e-02 5.732357e-03 -6.742522e-04 [16] -2.593319e-05 $lpf[[2]] [1] 2.859407e-06 1.907454e-06 -2.990384e-03 -1.980900e-03 3.355466e-02 [6] 7.702384e-03 -7.708457e-02 2.329811e-01 7.574938e-01 5.883470e-01 [11] 5.170879e-03 -1.352010e-01 -9.196125e-03 1.548964e-02 1.556956e-04 [16] -2.333987e-04 > > > > cleanEx() > nameEx("hosking.sim") > ### * hosking.sim > > flush(stderr()); flush(stdout()) > > ### Name: hosking.sim > ### Title: Generate Stationary Gaussian Process Using Hosking's Method > ### Aliases: hosking.sim > ### Keywords: ts > > ### ** Examples > > dB <- function(x) 10 * log10(x) > per <- function (z) { + n <- length(z) + (Mod(fft(z))^2/(2 * pi * n))[1:(n%/%2 + 1)] + } > spp.sdf <- function(freq, delta, omega) + abs(2 * (cos(2*pi*freq) - cos(2*pi*omega)))^(-2*delta) > data(acvs.andel8) > n <- 1024 > ## Not run: > ##D z <- hosking.sim(n, acvs.andel8[,2]) > ##D per.z <- 2 * pi * per(z) > ##D par(mfrow=c(2,1), las=1) > ##D plot.ts(z, ylab="", main="Realization of a Seasonal Long-Memory Process") > ##D plot(0:(n/2)/n, dB(per.z), type="l", xlab="Frequency", ylab="dB", > ##D main="Periodogram") > ##D lines(0:(n/2)/n, dB(spp.sdf(0:(n/2)/n, .4, 1/12)), col=2) > ## End(Not run) > > > > cleanEx() > nameEx("modwt.2d") > ### * modwt.2d > > flush(stderr()); flush(stdout()) > > ### Name: modwt.2d > ### Title: Two-Dimensional Maximal Overlap Discrete Wavelet Transform > ### Aliases: modwt.2d imodwt.2d > ### Keywords: ts > > ### ** Examples > > ## Xbox image > data(xbox) > xbox.modwt <- modwt.2d(xbox, "haar", 2) > ## Level 1 decomposition > par(mfrow=c(2,2), pty="s") > image(xbox.modwt$LH1, col=rainbow(128), axes=FALSE, main="LH1") > image(xbox.modwt$HH1, col=rainbow(128), axes=FALSE, main="HH1") > frame() > image(xbox.modwt$HL1, col=rainbow(128), axes=FALSE, main="HL1") > ## Level 2 decomposition > par(mfrow=c(2,2), pty="s") > image(xbox.modwt$LH2, col=rainbow(128), axes=FALSE, main="LH2") > image(xbox.modwt$HH2, col=rainbow(128), axes=FALSE, main="HH2") > image(xbox.modwt$LL2, col=rainbow(128), axes=FALSE, main="LL2") > image(xbox.modwt$HL2, col=rainbow(128), axes=FALSE, main="HL2") > sum((xbox - imodwt.2d(xbox.modwt))^2) [1] 0 > > data(dau) > par(mfrow=c(1,1), pty="s") > image(dau, col=rainbow(128), axes=FALSE, main="Ingrid Daubechies") > sum(dau^2) [1] 1049732962 > dau.modwt <- modwt.2d(dau, "d4", 2) > ## Level 1 decomposition > par(mfrow=c(2,2), pty="s") > image(dau.modwt$LH1, col=rainbow(128), axes=FALSE, main="LH1") > image(dau.modwt$HH1, col=rainbow(128), axes=FALSE, main="HH1") > frame() > image(dau.modwt$HL1, col=rainbow(128), axes=FALSE, main="HL1") > ## Level 2 decomposition > par(mfrow=c(2,2), pty="s") > image(dau.modwt$LH2, col=rainbow(128), axes=FALSE, main="LH2") > image(dau.modwt$HH2, col=rainbow(128), axes=FALSE, main="HH2") > image(dau.modwt$LL2, col=rainbow(128), axes=FALSE, main="LL2") > image(dau.modwt$HL2, col=rainbow(128), axes=FALSE, main="HL2") > sum((dau - imodwt.2d(dau.modwt))^2) [1] 0 > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("modwt") > ### * modwt > > flush(stderr()); flush(stdout()) > > ### Name: modwt > ### Title: (Inverse) Maximal Overlap Discrete Wavelet Transform > ### Aliases: modwt imodwt > ### Keywords: ts > > ### ** Examples > > ## Figure 4.23 in Gencay, Selcuk and Whitcher (2001) > data(ibm) > ibm.returns <- diff(log(ibm)) > # Haar > ibmr.haar <- modwt(ibm.returns, "haar") > names(ibmr.haar) <- c("w1", "w2", "w3", "w4", "v4") > # LA(8) > ibmr.la8 <- modwt(ibm.returns, "la8") > names(ibmr.la8) <- c("w1", "w2", "w3", "w4", "v4") > # shift the MODWT vectors > ibmr.la8 <- phase.shift(ibmr.la8, "la8") > ## plot partial MODWT for IBM data > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.returns, axes=FALSE, ylab="", main="(a)") > for(i in 1:5) + plot.ts(ibmr.haar[[i]], axes=FALSE, ylab=names(ibmr.haar)[i]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.returns, axes=FALSE, ylab="", main="(b)") > for(i in 1:5) + plot.ts(ibmr.la8[[i]], axes=FALSE, ylab=names(ibmr.la8)[i]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("mra.2d") > ### * mra.2d > > flush(stderr()); flush(stdout()) > > ### Name: mra.2d > ### Title: Multiresolution Analysis of an Image > ### Aliases: mra.2d > ### Keywords: ts > > ### ** Examples > > ## Easy check to see if it works... > ## -------------------------------- > > x <- matrix(rnorm(32*32), 32, 32) > # MODWT > x.mra <- mra.2d(x, method="modwt") > x.mra.sum <- x.mra[[1]] > for(j in 2:length(x.mra)) + x.mra.sum <- x.mra.sum + x.mra[[j]] > sum((x - x.mra.sum)^2) [1] 5.409576e-12 > > # DWT > x.mra <- mra.2d(x, method="dwt") > x.mra.sum <- x.mra[[1]] > for(j in 2:length(x.mra)) + x.mra.sum <- x.mra.sum + x.mra[[j]] > sum((x - x.mra.sum)^2) [1] 7.260364e-12 > > > > cleanEx() > nameEx("mra") > ### * mra > > flush(stderr()); flush(stdout()) > > ### Name: mra > ### Title: Multiresolution Analysis of Time Series > ### Aliases: mra > ### Keywords: ts > > ### ** Examples > > ## Easy check to see if it works... > x <- rnorm(32) > x.mra <- mra(x) > ## IGNORE_RDIFF_BEGIN > sum(x - apply(matrix(unlist(x.mra), nrow=32), 1, sum))^2 [1] 2.242776e-29 > ## IGNORE_RDIFF_END > > ## Figure 4.19 in Gencay, Selcuk and Whitcher (2001) > data(ibm) > ibm.returns <- diff(log(ibm)) > ibm.volatility <- abs(ibm.returns) > ## Haar > ibmv.haar <- mra(ibm.volatility, "haar", 4, "dwt") > names(ibmv.haar) <- c("d1", "d2", "d3", "d4", "s4") > ## LA(8) > ibmv.la8 <- mra(ibm.volatility, "la8", 4, "dwt") > names(ibmv.la8) <- c("d1", "d2", "d3", "d4", "s4") > ## plot multiresolution analysis of IBM data > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.volatility, axes=FALSE, ylab="", main="(a)") > for(i in 1:5) + plot.ts(ibmv.haar[[i]], axes=FALSE, ylab=names(ibmv.haar)[i]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > par(mfcol=c(6,1), pty="m", mar=c(5-2,4,4-2,2)) > plot.ts(ibm.volatility, axes=FALSE, ylab="", main="(b)") > for(i in 1:5) + plot.ts(ibmv.la8[[i]], axes=FALSE, ylab=names(ibmv.la8)[i]) > axis(side=1, at=seq(0,368,by=23), + labels=c(0,"",46,"",92,"",138,"",184,"",230,"",276,"",322,"",368)) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("my.acf") > ### * my.acf > > flush(stderr()); flush(stdout()) > > ### Name: my.acf > ### Title: Autocovariance Functions via the Discrete Fourier Transform > ### Aliases: my.acf my.ccf > ### Keywords: ts > > ### ** Examples > > data(ibm) > ibm.returns <- diff(log(ibm)) > plot(1:length(ibm.returns) - 1, my.acf(ibm.returns), type="h", + xlab="lag", ylab="ACVS", main="Autocovariance Sequence for IBM Returns") > > > > cleanEx() > nameEx("ortho.basis") > ### * ortho.basis > > flush(stderr()); flush(stdout()) > > ### Name: ortho.basis > ### Title: Derive Orthonormal Basis from Wavelet Packet Tree > ### Aliases: ortho.basis > ### Keywords: ts > > ### ** Examples > > data(japan) > J <- 4 > wf <- "mb8" > japan.mra <- mra(log(japan), wf, J, boundary="reflection") > japan.nomean <- + ts(apply(matrix(unlist(japan.mra[-(J+1)]), ncol=J, byrow=FALSE), 1, sum), + start=1955, freq=4) > japan.nomean2 <- ts(japan.nomean[42:169], start=1965.25, freq=4) > plot(japan.nomean2, type="l") > japan.dwpt <- dwpt(japan.nomean2, wf, 6) > japan.basis <- + ortho.basis(portmanteau.test(japan.dwpt, p=0.01, type="other")) > # Not implemented yet > # par(mfrow=c(1,1)) > # plot.basis(japan.basis) > > > > cleanEx() > nameEx("qmf") > ### * qmf > > flush(stderr()); flush(stdout()) > > ### Name: qmf > ### Title: Quadrature Mirror Filter > ### Aliases: qmf > ### Keywords: ts > > ### ** Examples > > ## Haar wavelet filter > g <- wave.filter("haar")$lpf > qmf(g) [1] 0.7071068 -0.7071068 > > > > cleanEx() > nameEx("sdf") > ### * sdf > > flush(stderr()); flush(stdout()) > > ### Name: Spectral Density Functions > ### Title: Spectral Density Functions for Long-Memory Processes > ### Aliases: fdp.sdf spp.sdf spp2.sdf sfd.sdf > ### Keywords: ts > > ### ** Examples > > dB <- function(x) 10 * log10(x) > > fdp.main <- expression(paste("FD", group("(",d==0.4,")"))) > sfd.main <- expression(paste("SFD", group("(",list(s==12, d==0.4),")"))) > spp.main <- expression(paste("SPP", + group("(",list(delta==0.4, f[G]==1/12),")"))) > > freq <- 0:512/1024 > > par(mfrow=c(2,2), mar=c(5-1,4,4-1,2), col.main="darkred") > plot(freq, dB(fdp.sdf(freq, .4)), type="l", xlab="frequency", + ylab="spectrum (dB)", main=fdp.main) > plot(freq, dB(spp.sdf(freq, .4, 1/12)), type="l", xlab="frequency", + ylab="spectrum (dB)", font.main=1, main=spp.main) > plot(freq, dB(sfd.sdf(freq, 12, .4)), type="l", xlab="frequency", + ylab="spectrum (dB)", main=sfd.main) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("shift.2d") > ### * shift.2d > > flush(stderr()); flush(stdout()) > > ### Name: shift.2d > ### Title: Circularly Shift Matrices from a 2D MODWT > ### Aliases: shift.2d > ### Keywords: ts > > ### ** Examples > > n <- 512 > G1 <- G2 <- dnorm(seq(-n/4, n/4, length=n)) > G <- 100 * zapsmall(outer(G1, G2)) > G <- modwt.2d(G, wf="la8", J=6) > k <- 50 > xr <- yr <- trunc(n/2) + (-k:k) > par(mfrow=c(3,3), mar=c(1,1,2,1), pty="s") > for (j in names(G)[1:9]) { + image(G[[j]][xr,yr], col=rainbow(64), axes=FALSE, main=j) + } > Gs <- shift.2d(G) > for (j in names(G)[1:9]) { + image(Gs[[j]][xr,yr], col=rainbow(64), axes=FALSE, main=j) + } > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("spin.covariance") > ### * spin.covariance > > flush(stderr()); flush(stdout()) > > ### Name: spin.covariance > ### Title: Compute Wavelet Cross-Covariance Between Two Time Series > ### Aliases: spin.covariance spin.correlation > ### Keywords: ts > > ### ** Examples > > ## Figure 7.9 from Gencay, Selcuk and Whitcher (2001) > data(exchange) > returns <- diff(log(exchange)) > returns <- ts(returns, start=1970, freq=12) > wf <- "d4" > demusd.modwt <- modwt(returns[,"DEM.USD"], wf, 8) > demusd.modwt.bw <- brick.wall(demusd.modwt, wf) > jpyusd.modwt <- modwt(returns[,"JPY.USD"], wf, 8) > jpyusd.modwt.bw <- brick.wall(jpyusd.modwt, wf) > n <- dim(returns)[1] > J <- 6 > lmax <- 36 > returns.cross.cor <- NULL > for(i in 1:J) { + blah <- spin.correlation(demusd.modwt.bw[[i]], jpyusd.modwt.bw[[i]], lmax) + returns.cross.cor <- cbind(returns.cross.cor, blah) + } > returns.cross.cor <- ts(as.matrix(returns.cross.cor), start=-36, freq=1) > dimnames(returns.cross.cor) <- list(NULL, paste("Level", 1:J)) > lags <- length(-lmax:lmax) > lower.ci <- tanh(atanh(returns.cross.cor) - qnorm(0.975) / + sqrt(matrix(trunc(n/2^(1:J)), nrow=lags, ncol=J, byrow=TRUE) + - 3)) > upper.ci <- tanh(atanh(returns.cross.cor) + qnorm(0.975) / + sqrt(matrix(trunc(n/2^(1:J)), nrow=lags, ncol=J, byrow=TRUE) + - 3)) > par(mfrow=c(3,2), las=1, pty="m", mar=c(5,4,4,2)+.1) > for(i in J:1) { + plot(returns.cross.cor[,i], ylim=c(-1,1), xaxt="n", xlab="Lag (months)", + ylab="", main=dimnames(returns.cross.cor)[[2]][i]) + axis(side=1, at=seq(-36, 36, by=12)) + lines(lower.ci[,i], lty=1, col=2) + lines(upper.ci[,i], lty=1, col=2) + abline(h=0,v=0) + } > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("squared.gain") > ### * squared.gain > > flush(stderr()); flush(stdout()) > > ### Name: squared.gain > ### Title: Squared Gain Function of a Filter > ### Aliases: squared.gain > ### Keywords: ts > > ### ** Examples > > par(mfrow=c(2,2)) > f.seq <- "H" > plot(0:256/512, squared.gain("d4", f.seq), type="l", ylim=c(0,2), + xlab="frequency", ylab="L = 4", main="Level 1") > lines(0:256/512, squared.gain("fk4", f.seq), col=2) > lines(0:256/512, squared.gain("mb4", f.seq), col=3) > abline(v=c(1,2)/4, lty=2) > legend(-.02, 2, c("Daubechies", "Fejer-Korovkin", "Minimum-Bandwidth"), + lty=1, col=1:3, bty="n", cex=1) > f.seq <- "HL" > plot(0:256/512, squared.gain("d4", f.seq), type="l", ylim=c(0,4), + xlab="frequency", ylab="", main="Level 2") > lines(0:256/512, squared.gain("fk4", f.seq), col=2) > lines(0:256/512, squared.gain("mb4", f.seq), col=3) > abline(v=c(1,2)/8, lty=2) > f.seq <- "H" > plot(0:256/512, squared.gain("d8", f.seq), type="l", ylim=c(0,2), + xlab="frequency", ylab="L = 8", main="") > lines(0:256/512, squared.gain("fk8", f.seq), col=2) > lines(0:256/512, squared.gain("mb8", f.seq), col=3) > abline(v=c(1,2)/4, lty=2) > f.seq <- "HL" > plot(0:256/512, squared.gain("d8", f.seq), type="l", ylim=c(0,4), + xlab="frequency", ylab="", main="") > lines(0:256/512, squared.gain("fk8", f.seq), col=2) > lines(0:256/512, squared.gain("mb8", f.seq), col=3) > abline(v=c(1,2)/8, lty=2) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("wave.variance") > ### * wave.variance > > flush(stderr()); flush(stdout()) > > ### Name: wave.variance > ### Title: Wavelet Analysis of Univariate/Bivariate Time Series > ### Aliases: wave.variance wave.covariance wave.correlation > ### Keywords: ts > > ### ** Examples > > ## Figure 7.3 from Gencay, Selcuk and Whitcher (2001) > data(ar1) > ar1.modwt <- modwt(ar1, "haar", 6) > ar1.modwt.bw <- brick.wall(ar1.modwt, "haar") > ar1.modwt.var2 <- wave.variance(ar1.modwt.bw, type="gaussian") > ar1.modwt.var <- wave.variance(ar1.modwt.bw, type="nongaussian") > par(mfrow=c(1,1), las=1, mar=c(5,4,4,2)+.1) > matplot(2^(0:5), ar1.modwt.var2[-7,], type="b", log="xy", + xaxt="n", ylim=c(.025, 6), pch="*LU", lty=1, col=c(1,4,4), + xlab="Wavelet Scale", ylab="") > matlines(2^(0:5), as.matrix(ar1.modwt.var)[-7,2:3], type="b", + pch="LU", lty=1, col=3) > axis(side=1, at=2^(0:5)) > legend(1, 6, c("Wavelet variance", "Gaussian CI", "Non-Gaussian CI"), + lty=1, col=c(1,4,3), bty="n") > > ## Figure 7.8 from Gencay, Selcuk and Whitcher (2001) > data(exchange) > returns <- diff(log(as.matrix(exchange))) > returns <- ts(returns, start=1970, freq=12) > wf <- "d4" > J <- 6 > demusd.modwt <- modwt(returns[,"DEM.USD"], wf, J) > demusd.modwt.bw <- brick.wall(demusd.modwt, wf) > jpyusd.modwt <- modwt(returns[,"JPY.USD"], wf, J) > jpyusd.modwt.bw <- brick.wall(jpyusd.modwt, wf) > returns.modwt.cov <- wave.covariance(demusd.modwt.bw, jpyusd.modwt.bw) > par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) > matplot(2^(0:(J-1)), returns.modwt.cov[-(J+1),], type="b", log="x", + pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", + ylab="Wavelet Covariance") > axis(side=1, at=2^(0:7)) > abline(h=0) > > returns.modwt.cor <- wave.correlation(demusd.modwt.bw, jpyusd.modwt.bw, + N = dim(returns)[1]) Warning in sqrt(n - 3) : NaNs produced Warning in sqrt(n - 3) : NaNs produced > par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) > matplot(2^(0:(J-1)), returns.modwt.cor[-(J+1),], type="b", log="x", + pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", + ylab="Wavelet Correlation") > axis(side=1, at=2^(0:7)) > abline(h=0) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("wavelet.filter") > ### * wavelet.filter > > flush(stderr()); flush(stdout()) > > ### Name: wavelet.filter > ### Title: Higher-Order Wavelet Filters > ### Aliases: wavelet.filter > ### Keywords: ts > > ### ** Examples > > ## Figure 4.14 in Gencay, Selcuk and Whitcher (2001) > par(mfrow=c(3,1), mar=c(5-2,4,4-1,2)) > f.seq <- "HLLLLL" > plot(c(rep(0,33), wavelet.filter("mb4", f.seq), rep(0,33)), type="l", + xlab="", ylab="", main="D(4) in black, MB(4) in red") > lines(c(rep(0,33), wavelet.filter("d4", f.seq), rep(0,33)), col=2) > plot(c(rep(0,35), -wavelet.filter("mb8", f.seq), rep(0,35)), type="l", + xlab="", ylab="", main="D(8) in black, -MB(8) in red") > lines(c(rep(0,35), wavelet.filter("d8", f.seq), rep(0,35)), col=2) > plot(c(rep(0,39), wavelet.filter("mb16", f.seq), rep(0,39)), type="l", + xlab="", ylab="", main="D(16) in black, MB(16) in red") > lines(c(rep(0,39), wavelet.filter("d16", f.seq), rep(0,39)), col=2) > > > > graphics::par(get("par.postscript", pos = 'CheckExEnv')) > cleanEx() > nameEx("wpt.test") > ### * wpt.test > > flush(stderr()); flush(stdout()) > > ### Name: wpt.test > ### Title: Testing the Wavelet Packet Tree for White Noise > ### Aliases: cpgram.test css.test entropy.test portmanteau.test > ### Keywords: ts > > ### ** Examples > > data(mexm) > J <- 6 > wf <- "la8" > mexm.dwpt <- dwpt(mexm[-(1:4)], wf, J) > ## Not implemented yet > ## plot.dwpt(x.dwpt, J) > mexm.dwpt.bw <- dwpt.brick.wall(mexm.dwpt, wf, 6, method="dwpt") > mexm.tree <- ortho.basis(portmanteau.test(mexm.dwpt.bw, p=0.025)) > ## Not implemented yet > ## plot.basis(mexm.tree) > > > > ### *