Learning Markov Processes with Latent Variables

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.