Long-Range Dependence Parameter Estimation For Mixed Spectra Gaussian Processes

We present an algorithm to estimate the Hurst parameter, H, in processes with mixed spectra. We focus on the two most studied Gaussian Long-Range Dependent (GLRD) processes: fractional Gaussian noise, fGn(H), and fractional integrated, FI(H), with Gaussian innovations. Our method consists in the decomposition of signal and noise components of the processes under analysis: first, we use harmonic analysis for detection of line components; second, we remove the line components mixed with the GLRD using information from their amplitudes iteratively; and finally, we use a robust method for the estimation of the LRD parameter, H. We apply the method to synthetic periodic time series, and numerical results are presented. The technique is applied to stock-market trading volume time series.