waveslim (version 1.12)

spin.covariance: 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

x

first time series

y

second time series, same length as x

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) 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, Journal of Geophysical Research, 105, No. D11, 14,941-14,962.

See Also

wave.covariance, 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)
}