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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 χ2 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%. [ABSTRACT FROM AUTHOR]

In this paper we make use of the multiresolution properties of discrete wavelets, including their ability to remove interference, to reveal closely spaced spectral peaks. We propose a procedure which we first verify on two test signals, and then apply it to the time series of homogeneous Indian monsoon rainfall annual data. We show that, compared to empirical mode decomposition, discrete wavelet analysis is more effective in identifying closely spaced frequencies if used in combination with classical power spectral analysis of wavelet-based partially reconstructed time series. An effective criterion based on better localization of specific frequency components and accurate estimation of their amplitudes is used to select an appropriate wavelet. It is shown here that the discrete Meyer wavelet has the best frequency properties among the wavelet families considered (Haar, Daubechies, Coiflet and Symlet). In rainfall data, the present analysis reveals two additional spectral peaks besides the fifteen found by classical spectral analysis. Moreover, these two new peaks have been found to be statistically significant, although a detailed discussion of testing for significance is being presented elsewhere. [ABSTRACT FROM AUTHOR]