  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 $\lambda$ 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 $[\lambda^{n-1}, \lambda^n)$, $n\in
\mathbb{N}$. 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. We also present a new efficient method for estimation
of Hurst parameter of selfsimilar processes. As an example we introduce simple
fractional Brownian motion (sfBm) which is semi-selfsimilar with stationary
increments. We present some simulations and numerical evaluation to illustrate
the results and to estimate the scale for sfBm as a semi-selfsimilar process.
We also present another simulation and show the efficiency of our method in
estimation of Hurst parameter by comparing its performance with some previous
methods.
