Wavelets for time series analysis - a survey and new results
Jan Mielniczuk, Piotr Wojdyłło · 2005
Abstract: In the paper we review stochastic properties of wavelet coefficients for time series indexed either by continuous or discrete time. The main emphasis is on a decorrelation property and its implications for data analysis. Some new properties are developed as the rates of the correlation decay for the wavelet coefficients in the case of long-range dependent processes such as the fractional Gaussian noise and the fractional autoregressive integrated moving average processes. It is proved that for such processes the within-scale covariance of the wavelet coefficents at lag k is O(k2(H−N)−2), where H is the Hurst exponent and N is the number of vanishing moments of the wavelet employed. Some applications of decorrelation property are briefly discussed.