Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multifractal detrended fluctuation analysis (MF-DFA) method and is quite accurate for small size data sets. As compared to polynomial fits in the MF-DFA, a single Daubechies wavelet is used here for detrending purposes. The natural, built-in variable window size in wavelet transforms makes this procedure well suited for non-stationary data. We illustrate the working of this method through the analysis of binomial multifractal model. For this model, our results compare well with those calculated analytically and obtained numerically through MF-DFA. To show the efficacy of this approach for finite data sets, we also do the above comparison for Gaussian white noise time series of different sizes. In addition, we analyze time series of three experimental data sets of tokamak plasma and also spin density fluctuations in 2D Ising model.