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Periodically homogeneous Markov chains: The discrete state space case

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  • Aknouche, Abdelhakim

Abstract

state spaces with periodically time-varying transition probabilities is introduced. The finite-dimensional probability distributions of these time-periodic chains are first studied and their correspondence with the marginal distributions and transition probabilities is shown. Then, the concepts of periodic stability/regularity and limiting behaviors are proposed. The communicability and classification of states necessary for establishing periodic stability are then examined. In particular, periodic irreducibility and the main solidarity/class properties are presented, namely periodic recurrence, periodic positive recurrence, periodic transience, and periodic aperiodicity. Furthermore, sufficient conditions for periodic stochastic stability of time-periodic Markov chains are derived. Finally, various applications to some operations research models and time series analysis are considered. In particular, periodic Markov decision processes, periodic integer-valued time series models, and periodic Markov-switching time series models are examined.

Suggested Citation

  • Aknouche, Abdelhakim, 2024. "Periodically homogeneous Markov chains: The discrete state space case," MPRA Paper 122287, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:122287
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    References listed on IDEAS

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    Cited by:

    1. Aknouche, Abdelhakim & Bentarzi, Mohamed, 2025. "Efficient two-stage estimation of cyclical ARCH models," MPRA Paper 127417, University Library of Munich, Germany.

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    JEL classification:

    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C30 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - General

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