Estimation of the self-similarity parameter in long memory processes

Abstract

Long memory processes, where positive correlations between observations far apart in time and space decay very slowly to zero with increasing time lag, occur quite frequently in fields such as hydrology and economics. Stochastic processes that are invariant in distribution under judicious scaling of time and space, called self-similar process, can parsimoniously model the long-run properties of phenomena exhibiting long-range dependence. Four of the heuristic estimation approaches have been presented in this study so that the self-similarity parameter, H that gives the correlation structure in long memory processes, can be effectively estimated. Finally, the methods presented in this paper were applied to two observed time series, namely Nile River Data set and the VBR (Variable- Bit-Rate) data set. The estimated values of H for two data sets found from different methods suggest that all methods are not equally good for estimation.

Keywords: Long memory process, long-range dependence, Self-similar process, Hurst Parameter, Gaussian noise.

DOI: 10.3329/jme.v38i0.898

Journal of Mechanical Engineering Vol.38 Dec. 2007 pp.32-37