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The problem of estimation of the Hurst parameter for self-similar time series is discussed in the paper. Five methods of estimation of the Hurst parameter for prices of MSFT ticker, for returns of MSFT ticker and for simulated FARIMA time series with  H  = 0.766 are presented. Methods that are inefficient for estimation the Hurst parameter in limit cases ( H  close to 0.5 and  H  close to 1) are detected based on the presented methods. The long-range dependence of the mentioned three time series are statistically proved.

Long-range dependence of time series for MSFT data of the prices of shares and returns