M. Malyutov, T. Zhang, Yi Li, and X. Li

Time series homogeneity tests via VLMC training

J. Rissanen modified Markov Chains of memory length n by assuming that the current state of a string is independent of the symbols in its past preceding a context of the length which is a function of the past itself. He developed a construction algorithm of contexts stochastic suffix tree for compressing stationary time series and proved its consistency. Rissanen's Variable memory Length Markov Chains (VLMC) were formally applied for classifying non-stationary proteins by G. Bejerano and others by training their VLMC models.

In this paper, we apply VLMC training of presumably stationary parts of piece-wise stationary time series for testing homogeneity of longer regions and, if homogeneity is rejected, for identifying most discriminating contexts.

КЛЮЧЕВЫЕ СЛОВА: Variable memory Length Markov Chain, log-likelihood, approximate likelihood ratio homogeneity test, mining for most distinguishing contexts