modwt.vt: Variance Transformation Operation - MODWT

In zejiang-unsw/WASP_1.0.0: WAvelet System Prediction

Description

Variance Transformation Operation - MODWT

Usage

modwt.vt(
  data,
  wf,
  J,
  pad,
  boundary,
  vt.opt = c("Sxx", "Cov"),
  cov.opt = c("auto", "pos", "neg")
)

Arguments

data	A list of response x and dependent variables dp.
wf	Name of the wavelet filter to use in the decomposition.
J	Specifies the depth of the decomposition. This must be a number less than or equal to log(length(x),2).
pad	The method used for extend data to dyadic size. Use "per", "zero", or "sym".
boundary	Character string specifying the boundary condition. If boundary=="periodic" the default, then the vector you decompose is assumed to be periodic on its defined interval, if boundary=="reflection", the vector beyond its boundaries is assumed to be a symmetric reflection of itself.
vt.opt	Options of variance transformation matrix, either "Sxx" or "Cov".
cov.opt	Options of Covariance matrix sign. Use "pos", "neg", or "auto".

Value

A list of 8 elements: wf, vt.opt, boundary, pad, x (data), dp (data), dp.n (variance trasnformed dp), and S (covariance matrix).

References

Z Jiang, A Sharma, and F Johnson. WRR

Percival, D. B. and A. T. Walden (2000) Wavelet Methods for Time Series Analysis, Cambridge University Press.

Examples

###real-world example
x <- window(SPI.12,start=c(1950,1),end=c(2009,12))
dp <- window(obs.mon,start=c(1950,1),end=c(2009,12))
vt.opt = ifelse(0,"Sxx","Cov")

for(id in 5){

  data <- list(x=x[,id],dp=dp)
  dwt <- modwt.vt(data, wf="d4", J=7, pad="zero", boundary="periodic", vt.opt)

  par(mfrow=c(ncol(dp),1),pty="m",mar=c(1,4,1,2))
  for(i in 1:ncol(dp))
    ts.plot(dwt$dp[,i],dwt$dp.n[,i],xlab=NA,col=c("black","red"),lwd=c(2,1))
}
###synthetic example
#frequency, sampled from a given range
fd <- c(3,5,10,15,25,30,55,70,95)

data.SW1 <- data.gen.SW(nobs=512,fp=25,fd=fd)
dwt.SW1 <- modwt.vt(data.SW1, wf="d4", J=7, pad="zero", boundary="periodic",vt.opt)

x.modwt <- waveslim::modwt(dwt.SW1$x, wf = "d4", n.levels = 7,  boundary = "periodic")
dp.modwt <- waveslim::modwt(dwt.SW1$dp[,1], wf = "d4", n.levels = 7,  boundary = "periodic")
dp.vt.modwt <- waveslim::modwt(dwt.SW1$dp.n[,1], wf = "d4", n.levels = 7, boundary = "periodic")

sum(sapply(dp.modwt,var)); var(dwt.SW1$dp[,1])
sum(sapply(dp.vt.modwt,var)); var(dwt.SW1$dp.n[,1])

data <- rbind(sapply(dp.modwt,var)/sum(sapply(dp.modwt,var)),
              sapply(dp.vt.modwt,var)/sum(sapply(dp.vt.modwt,var)))

par(mfrow=c(1,1))
bar <- barplot(data, beside = T, col=c("red","blue"))
lines(x = bar[2,], y = sapply(x.modwt,var)/sum(sapply(x.modwt,var)))
points(x = bar[2,], y = sapply(x.modwt,var)/sum(sapply(x.modwt,var)))

zejiang-unsw/WASP_1.0.0 documentation built on May 6, 2020, 7:49 p.m.