Wavelets for time series analysis – A survey and new results

In the paper the stochastic properties of wavelet coefficients for time series, indexed by continuous or discrete time, are reviewed. The main emphasis is on decorrelation property and its implications for data analysis. Some new properties are developed as the rates of 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 demonstrated that for such processes the within–scale covariance of the wavelet coefficients at lag is , where is the Hurst exponent and is the number of vanishing moments of the wavelet employed. Some applications of the decorrelation property are briefly discussed.