Power Laws in Financial Time Series

We attempt empirical detection and characterization of power laws in financial time series. Fractional Brownian motion is defined. After testing for multifractality we calculate the multifractal spectrum of the series. The multifractal nature of stock prices leads to volatility clus-tering (conditional heteroscedasticity) and long memory (slowly decaying autocorrelation). Wavelet Transform Modulus Maxima approach to mul-tifractal spectrum estimation proved certain advantages to the structure function approach as shown by Muzy et al. (1993). We apply wavelet based methodology as wavelets are an appropriate tool for non-stationary time series