INVESTIGATING MULTIFRACTALITY OF STOCK MARKET FLUCTUATIONS USING WAVELET AND DETRENDING FLUCTUATION METHODS

摘要

We apply the Multifractal Detrended Fluctuation Analysis and the Wavelet Transform Modulus Maxima to investigate multifractal properties of stock price fluctuations. By applying both methods to the same data sets coming from the German and the American stock markets and based on our earlier knowledge of how these methods detect multifractal-ity while employed to well-known mathematical models, we compare the results given by both methods and infer which one can be preferable in the case of the financial data. We argue that the Multifractal Detrended Fluctuation Analysis acts better for a global detection of multifractal behavior, while the Wavelet Transform Modulus Maxima method is the optimal tool for the local characterization of the scaling properties of signals.