B. J Whitcher, P. Guttorp and D. B. Percival (2000), `Wavelet Analysis of Covariance with Application to Atmospheric Time Series,' Journal of Geophysical Research, 105, no. D11, pp. 14,941-62.
Multi-scale analysis of univariate time series has appeared in the literature at an ever increasing rate. Here we discuss the multi-scale 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. An analysis of El-Nio--Southern Oscillation events and the Madden-Julian oscillation is performed using a 35+ year record. We show how potentially complicated patterns of cross-correlation are easily decomposed using the wavelet cross-correlation on a scale by scale basis, where each wavelet cross-correlation series is associated with a specific physical time scale.
Go to next summary or to home page for Don Percival