Innovative Method for Estimating Scale Parameter of Semi-Selfsimilar Processes

Innovative Method for Estimating Scale Parameter of Semi-Selfsimilar Processes

The characteristic feature of semi-selfsimilar process is the invariance of its finite dimensional distributions by certain dilation for specific scaling factor. Estimating the scale parameter A and the Hurst index of such processes is one of the fundamental problem in the literature. We present some iterative method for estimation of the scale and Hurst parameters which is addressed for semi-selfsimilar processes with stationary increments. This method is based on some flexible sampling scheme and evaluating sample variance of increments in each scale intervals. For such iterative method we find the initial estimation for the scale parameter by evaluating cumulative sum of moving sample variances and also by evaluating sample variance of preceding and succeeding moving sample variance of increments. As an example we introduce simple fractional Brownian motion (sfBm) which is semiselfsimilar with stationary increments. We present some simulations and Intimerical evaluation to illustrate the results and to estimate the scale for sfBm as a semi-selfsimilar process.