Zusammenfassung
Multiscale analysis of univariate time series has appeared in the
literature at an ever increasing rate. Here we introduce the multiscale
analysis of covariance between two time series using the discrete
wavelet transform. The wavelet covariance and wavelet correlation
are defined and applied to this problem as an alternative to traditional
cross-spectrum analysis. The wavelet covariance is shown to decompose
the covariance between two stationary processes on a scale by scale
basis. Asymptotic normality is established for estimators of the
wavelet; covariance and correlation. Both quantities are generalized
into the wavelet cross covariance and cross correlation in order
to investigate possible lead/lag relationships. A thorough analysis
of interannual variability for the Madden-Julian oscillation is performed
using a 35+ year record of daily station pressure series. The time
localization of the discrete wavelet transform allows the subseries,
which are associated with specific physical time scales, to be partitioned
into both seasonal periods (such as summer and winter) and also according
to El Nine-Southern Oscillation (ENSO) activity, Differences in variance
and correlation between these periods may then be firmly established
through statistical hypothesis testing. The daily station pressure
series used here show clear evidence of increased variance and correlation
in winter across Fourier periods of 16-128 days, During warm episodes
of ENSO activity, a reduced variance is observed across Fourier periods
of 8-512 days for the station pressure series from Truk Island and
little or no correlation between station pressure series for the
same periods.
Nutzer