Working paper

Learning Markov Processes with Latent Variables

Ayden Higgins, and Koen Jochmans

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.

Keywords

Dynamic discrete choice; finite mixture; Markov process; regime switching; state dependence;

JEL codes

  • C32: Time-Series Models • Dynamic Quantile Regressions • Dynamic Treatment Effect Models • Diffusion Processes
  • C33: Panel Data Models • Spatio-temporal Models
  • C38: Classification Methods • Cluster Analysis • Principal Components • Factor Models

Reference

Ayden Higgins, and Koen Jochmans, “Learning Markov Processes with Latent Variables”, TSE Working Paper, n. 22-1366, September 2022, revised December 2024.

See also

Published in

TSE Working Paper, n. 22-1366, September 2022, revised December 2024