Wavelet Frequency Domain Approach for Statistical Modeling of Rainfall Time-Series Data

Abstract

The powerful methodology of “Wavelet analysts in frequency domain” for analyzing time-series data is studied. As an illustration, Indian monsoon rainfall time-series data from 1879–2006 is considered. The entire data analysis is carried out using SPLUS WAVELET TOOLKIT software package. The discrete wavelet transform (DWT) and multiresolution analysis (MRA) of the data are computed to analyze the behaviour of trend present in the time-series data in terms of different times and scales. By using bootstrap method, size and power of the test for testing significance of trend in the data is computed. It is found that the size of the test for Daubechies wavelet is more than that for Haar wavelet. In respect of both Daubechies and Haar wavelet filtere, it is found that the test for presence of trend is unbiased. Also, power of the test for both Daubechies (D4) and Haar wavelets, at level 5 is less than the one at level 6. Further, Haar wavelet at level 6 has generally performed better than Daubechies (D4) wavelet at level 6 in terms of power of the test. Using the former wavelet, a declining trend in the data under consideration is revealed.