[R] Wavelets correlation test

[Brandon Whitcher]

> Hello, I use wavethresh packages to perform wavelet analysis. In
> particular, I would like to compare 2 signals (vectors) after a wavelet
> decomposition. I would like to use cor.test function, but this function
> acts on the entire vector values. I plan to perform a cor.test on each
> level of the wavelet decomposition, say N. So I will have at the end of
> a first step N results of cor.test.
>
> How can I deal with this N results to have an answer globaly ?

A lot of this code is already implemented in an alternative wavelet
analysis package for R (waveslim).  There, I have placed code to compute
multiscale covariance/correlation estimates that may also be a function of
lag.  This would provide a correlation coefficient (or autocorrelation
sequence) per scale.  Approximate confidence intervals for these estimates
are also available, there might be a reference in wave.covariance or
wave.correlation -- I can't remember.  The papers of interest are:

- Whitcher, Guttorp, Percival (2000).  Wavelet analysis of covariance with
application to atmospheric time series, JGR 105 (D11), 14,941-14,962.

- Serroukh and Walden (2000).  Wavelet scale analysis of bivariate time
series I: Motivation and estimation, Journal of Nonparametric Statistics,
13 (1), 1-36.

- Gencay, Selcuk, Whitcher (2001).  An Introduction to Wavelets and Other
Filtering Methods in Finance and Economics, Academic Press.

I think it would be difficult to make a statement for the whole series.
Some scales may agree and some scales may not.  What is the scientific
question you are trying to answer?

cheers...

Brandon

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