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Abstract:
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Finitely-valued stationary time series are described by the collection of the conditional probabilities of the possible values given the infinite pasts. The concept of context is extended to be an arbitrary part - not necessarily a continuous ending - of the past that determines the transition probability. The context set model of the time series consists of the collection of all contexts and the corresponding transition probabilities. Based on a sample of length n, the estimated context set is defined via optimizing the Bayesian Information Criterion (BIC) over all possible context set models. An algorithm is shown to calculate the estimator in feasible time despite the very large number of possible models, and the context set estimator is studied on a standard data set.
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