SCOT modeling, training and Homogeneity testing

M. Malyutov, P. Grosu and T. Zhang

Abstract

Stochastic COntext Tree (abbreviated as SCOT) is m-Markov Chain (m-MC) with every state of a string independent of the symbols in its more remote past than the {\bf context} of {\bf length} determined by the preceding symbols of this state. We model and apply SCOT for statistical inference about financial, literary and seismological stationary strings in `Information processes’, vol13, No4, Vol 14, No. 3 and volume 15, No.1, available online. . SCOT construction is also used for compression under various names VLMC, VOMC, PST, CTW. Apparently, G. Bejerano (2003) made the first SCOT Statistical Likelihood comparison application to non-stationary Bioinformatics data which seems inadequate. We evaluate SCOT contexts  stationary distribution iteratively in several  examples; analyze several models viewed as simplified approaches to financial modeling:, evaluate their stationary distribution, entropy rate and convergence to the Brownian motion. Financial applications showed advantage of SCOT –based testing homogeneity over GARCH.