An EM-Based Viterbi Approximation Algorithm for Mixed-State Latent Factor Models

In this article, a state-space model based on an underlying hidden Markov chain model (HMM) with factor analysis observation process is introduced. The HMM generates a piece-wise constant state evolution process and the observations are produced from the state vectors by a conditionally heteroscedastic factor analysis observation process. More specifically, we concentrate on situations where the factor variances are modeled by univariate Generalized Quadratic Autoregressive Conditionally Heteroscedastic processes (GQARCH). An expectation maximization (EM) algorithm combined with a mixed-state version of the Viterbi algorithm is derived for maximum likelihood estimation. The various regimes, common factors, and their volatilities are supposed unobservable and the inference must be carried out from the observable process. Extensive Monte Carlo simulations show promising results of the algorithms, especially for segmentation and tracking tasks.