Long memory processes with an application to data

Long-range dependence is a phenomenon that may arise in the analysis\ud of time series data. In long-memory processes, the autocorrelation function exhibits\ud power-like decay. The Hurst parameter H is a measure of the long-range dependence\ud in a time series. In our study we investigate long-memory processes and consider methods to estimate the Hurst parameter. We compare the performance of the existing methods of Aggravated Variance, Absolute Moments, Local Whittle and\ud Wavelets using simulations. We found that the Local Whittle and Wavelets methods\ud are superior. We apply these methods to the neonatal EEG-sleep data. During the\ud sleep there are different sleep stages - active and quiet. Our hypothesis is EEG\ud data of active sleep is a long-memory process. The local Whittle estimation of the\ud parameter H supports this hypothesis. The Wavelets method gives estimations of\ud the parameter H out of the bounds. Also, we analyze Ethernet data and found that\ud both methods support the hypothesis that Ethernet data is a long-memory process