Time-varying and Seasonal Analysis Using Hilbert Wavelet Pairs

Performs time-varying or seasonal coherence and phase anlaysis between two time seris using the maximal-overlap discrete Hilbert wavelet transform (MODHWT).

modhwt.coh(x, y, f.length = 0)
modhwt.phase(x, y, f.length = 0)
modhwt.coh.seasonal(x, y, S = 10, season = 365)
modhwt.phase.seasonal(x, y, season = 365)

Arguments

x	MODHWT object.
y	MODHWT object.
f.length	Length of the rectangular filter.
S	Number of "seasons".
season	Length of the "season".

Value

Time-varying or seasonal coherence and phase between two time series. The coherence estimates are between zero and one, while the phase estimates are between \(-\pi\) and \(\pi\).

Details

The idea of seasonally-varying spectral analysis (SVSA, Madden 1986) is generalized using the MODWT and Hilbert wavelet pairs. For the seasonal case, \(S\) seasons are used to produce a consistent estimate of the coherence and phase. For the non-seasonal case, a simple rectangular (moving-average) filter is applied to the MODHWT coefficients in order to produce consistent estimates.

References

Madden, R.A. (1986). Seasonal variation of the 40--50 day oscillation in the tropics. Journal of the Atmospheric Sciences\/ 43\/(24), 3138--3158.

Whither, B. and P.F. Craigmile (2004). Multivariate Spectral Analysis Using Hilbert Wavelet Pairs, International Journal of Wavelets, Multiresolution and Information Processing, to appear.

Author