means it also satisfies as , where is a finite positive constant independent of m, and 0<β<1. Estimating the self-similarity parameter "H" R/S analysis Assume that the underlying process is Fractional Gaussian Noise. Consider the series , and let . The sample variance of is Definition:R/S statistic If is FGN, then Consider fitting a regression model : , where In particular for a time series of length divide the time series data into groups each of size , compute for each group. Thus for each n we have pairs of data ().There are points for each , so we can fit a regression model to estimate more accurately. If the slope of the regression line is between 0.5~1, it is a self-similar process. Variance-time plot Variance of the sample mean is given by . For estimating H, calculate sample means for sub-series of length . Overall mean can be given by , sample variance . The variance-time plots are obtained by plotting against and we can fit a simple least square line through the resulting points in the plane ignoring the small values of k. For large values of , the points in the plot are expected to be scattered around a straight line with a negative slope .For short-range dependence or independence among the observations, the slope of the straight line is equal to -1. Self-similarity can be inferred from the values of the estimated slope which is asymptotically between –1 and 0, and an estimate for the degree of self-similarity is given by Periodogram-based analysis Whittle's approximate maximum likelihood estimator (MLE) is applied to solve the Hurst's parameter via the spectral density of . It is not only a tool for visualizing the Hurst's parameter, but also a method to do some statistical inference about the parameters via the asymptotic properties of the MLE. In particular, follows a Gaussian process. Let the spectral density of , , where , and construct a short-range time series autoregression (AR) model, that is , with . Thus, the Whittle's estimator of minimizes the function , where denotes the periodogram of X as and . These integrations can be assessed by Riemann sum. Then asymptotically follows a normal distribution if can be expressed as a form of an infinite moving average model. To estimate , first, one has to calculate this periodogram. Since is an estimator of the spectral density, a series