A wavelet based significance test for periodicities in Indian monsoon rainfall

This paper is a sequel to a recent study of the authors' that uses a combination of multiresolution analysis (MRA) and classical Fourier spectral methods, to identify 17 peaks in the power spectral density of the Homogeneous Indian Monsoon (HIM) rainfall time series constructed in Ref. 1. Here we propose a new procedure for testing the statistical significance of these peaks. In this procedure, using MRA the stationary component of the rainfall time series is first identified. Then (partially) reconstructed time series are derived over each scale band in the stationary component. For each of these time series an appropriately colored reference spectrum is derived. The significance of the detected peaks is then determined using a chi(2) test against the reference spectra, which together represent a noise process spectrally close to rainfall. It is concluded that HIM rainfall exhibits 10 statistically significant periodicities at a confidence level of 99.9%.