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LEARNING MARKOV PROCESSES WITH LATENT VARIABLES

Published online by Cambridge University Press:  13 February 2025

Ayden Higgins  and
Koen Jochmans
Ayden Higgins
Affiliation:
University of Exeter Business School
Koen Jochmans*
Affiliation:
Toulouse School of Economics
*
Address correspondence to Koen Jochmans, Toulouse School of Economics, Université Toulouse Capitole, Toulouse, France, e-mail: koen.jochmans@tse-fr.eu
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Abstract

We consider the problem of identifying the parameters of a time-homogeneous bivariate Markov chain when only one of the two variables is observable. We show that, subject to conditions that we spell out, the transition kernel and the distribution of the initial condition are uniquely recoverable (up to an arbitrary relabelling of the state space of the latent variable) from the joint distribution of four (or more) consecutive time-series observations. The result is, therefore, applicable to (short) panel data as well as to (stationary) time series data.

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ARTICLES
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Econometric Theory , First View , pp. 1 - 13
Copyright
© The Author(s), 2025. Published by Cambridge University Press

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Footnotes

We are grateful to Anna Mikusheva, Peter Phillips, and two anonymous referees for constructive feedback. Financial support from the European Research Council, grant ERC-2016-STG-715787, and from the French Government and the ANR under the Investissements d’ Avenir program, grant ANR-17-EURE-0010 is gratefully acknowledged.

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