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A point on discrete versus continuous state-space Markov chains

Author

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  • Muia Mathias

    (Department of Mathematics and Statistics, University of South Alabama, Mobile, Al 36688, United States of America)

  • Longla Martial

    (Department of Mathematics, University of Mississippi, University, MS 38677, United States of America)

Abstract

This article investigates the effects of discrete marginal distributions on copula-based Markov chains. We establish results on mixing properties and parameter estimation for a copula-based Markov chain model with Bernoulli( p p ) marginal distributions, emphasizing some distinctions between continuous and discrete state-space Markov chains. We derive parameter estimators using the maximum-likelihood estimation (MLE) method and explore alternative estimators of p p that are asymptotically equivalent to the MLE. Furthermore, we provide the asymptotic distributions of these parameter estimators. A simulation study is conducted to evaluate the performance of the various estimators for p p . Additionally, we employ the likelihood ratio test to assess independence within the sequence.

Suggested Citation

  • Muia Mathias & Longla Martial, 2025. "A point on discrete versus continuous state-space Markov chains," Dependence Modeling, De Gruyter, vol. 13(1), pages 1-23.
    • Handle: RePEc:vrs:demode:v:13:y:2025:i:1:p:23:n:1001
    DOI: 10.1515/demo-2025-0015
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