R: Compute Wavelet Cross-Covariance Between Two Time Series

spin.covariance {waveslim} | R Documentation

## 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)

### Details

See references.

### Value

List structure holding the wavelet cross-covariances (correlations) according to scale.

### Author(s)

B. Whitcher

### 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)
    }

[Package waveslim version 1.7.5 Index]