Learning Markov Processes with Latent Variables

Résumé

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.

Mots-clés

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

Codes JEL

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