  We illustrate the efficacy of a discrete wavelet based approach to
characterize fluctuations in non-stationary time series. The present approach
complements the multi-fractal 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 de-trending
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 multi-fractal 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 size. In addition, we analyze time series of three
experimental data sets of tokamak plasma and also spin density fluctuations in
2D Ising model.
