Statistical analysis of parsimonious high-order multivariate finite Markov chains based on sufficient statistics

Yuriy Kharin and Valeriy Voloshko

Journal of Multivariate Analysis, 2025, vol. 208, issue C

Abstract: A new parsimonious MCSS(s) (which stands for “Markov Chain of order s based on Sufficient Statistics”) model for multivariate discrete-valued time series is constructed. The MCSS(s) model has sufficient statistics of a simple form based on multivariate frequencies of (s+1)-tuples for observed time series. Special cases of the MCSS(s) model and their relations to the results known in the literature are discussed. The strong concavity property of the loglikelihood function and the uniqueness of the maximum likelihood estimator under mild regularity conditions are proven for the MCSS(s) model. Forecasting statistics for the multivariate discrete-valued time series derived with the MCSS(s) model are constructed. The developed theory is illustrated with computer experiments on simulated and real data.

Keywords: Efficient estimator; Exponential family; High-order Markov chain; Multivariate frequencies; Parsimonious model; Sufficient statistics (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1016/j.jmva.2025.105422

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