Distributions of pattern statistics in sparse Markov models
A time series \(\mathbf{X}\) that takes values in a finite set \(\Sigma\) is modelled by an \(m\)th-order Markov sequence; this may be embedded in a first-order Markov chain, at the price of specifying \(|\Sigma|^m\,(|\Sigma|-1)\) transition probabilities. Moreover Markov models allow fairly few choices for the number of model parameters. The author considers Sparse Markov Models (see Definition 1) which allow to group conditioning histories into classes such that the conditional probability distribution is constant for the members of each class. The methodology for efficient computation of pattern distributions is extended to the sparse Markov framework.
scientific article; zbMATH DE number 7223265
scientific article