Using the Wavelet Transform for Time Series Analysis

The characterization of time series requires knowledge of certain para- meters. One of those parameters is the Hurst exponent, which is an indicator of long-range dependence characteristics. Rescaled range (R/S), proposed by E. Hurst, is the most commonly used method to compute this exponent. On the other hand, wavelet analysis is known to reflect better the nonlinear dynamics of the biological, climatic, or economic series than the statistical tools often used for this analysis. The average wavelet coefficient (AWC) is a wavelet method that has been used for the last years to compute the Hurst exponent. In this paper, we present a modification to the AWC method, and we compare its performance with the original version of AWC and with R/S methods. The results obtained for the synthetic series were so promising that we decided to apply our proposal in rainfall series. Therefore, these results were compared with the ones reported from La Pampa. After that, series from different climatic regions of the Argentine Republic were analyzed.