Sunday, March 20, 2011

Wavelet Coherence Analysis!

I've started using a cool Matlab program that generates a 4-dimensional power spectra for any time series. A normal power spectra is averaged over an entire dataset, but this technique, called Wavelet Coherence Analysis using a sliding "window" to examine power spectra continuously over the entire series. Of course, for longer and longer wavelengths, the sliding window necessarily becomes larger and larger, until wavelengths can no longer be measured on the data. The dark black hemicurve on this diagram shows that limit, and the data greyed out beyond that line is edge-affected power spectra.

The data I chose for this analysis were the maximum daily temperatures for Chapel Hill, North Carolina, in 2010. There are 365 days along the X axis, and various wavelengths ranging from 4 to 64 days along the Y axis. Colors indicate "power" at a given wavelength, for a given time of the year. Significant areas within the hemicurve are circled with a black line.

This analysis shows that there were some 6-day cycles in springtime (near DOY 150) that were statistically significant. Beyond that, not much jumps out: the signal does now have high periodicity. Now I'm looking for better-behaving data.

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