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Learning markov processes with latent variables

Author

Listed:
  • Ayden Higgins

    (University of Exeter Business School - University of Exeter)

  • Koen Jochmans

    (TSE-R - Toulouse School of Economics - UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse - EHESS - École des hautes études en sciences sociales - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement, UT Capitole - Université Toulouse Capitole - Comue de Toulouse - Communauté d'universités et établissements de Toulouse)

Abstract

We present a constructive proof of (nonparametric) identication of the parameters of a bivariate Markov chain when only one of the two random variables is observable. This setup generalizes the hidden Markov model in various useful directions, allowing for state dependence in the observables and allowing the transition kernel of the hidden Markov chain to depend on past observables. We give conditions under which the transition kernel and the distribution of the initial condition are both identied (up to a permutation of the latent states) from the joint distribution of four (or more) time-series observations.

Suggested Citation

  • Ayden Higgins & Koen Jochmans, 2026. "Learning markov processes with latent variables," Post-Print hal-05488665, HAL.
    • Handle: RePEc:hal:journl:hal-05488665
    DOI: 10.1017/S0266466625000027
    Note: View the original document on HAL open archive server: https://hal.science/hal-05488665v1
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    References listed on IDEAS

    as
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    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C33 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Models with Panel Data; Spatio-temporal Models
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis

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