HWP Analysis: Time-varying and Seasonal Analysis Using Hilbert Wavelet Pairs

Description

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

Usage

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

MODHWT object.

f.length

Length of the rectangular filter.

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 $-$ and $$.
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.
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.
hilbert.filter[object Object] ts