ASYMPTOTIC PROPERTIES OF APPROXIMATE MAXIMUM LIKELIHOOD ESTIMATOR IN MARKOV-SWITCHING STATE-SPACE MODELS

For Markov-switching state-space models, it is practically infeasible to compute the likelihood function through the Kalman filter because of the path dependence on regimes. A widely applied approximation algorithm uses a collapsing step to average out the most dated regime and truncates the regime path. This algorithm’s performance, however, has not been examined analytically. This study fills the gap. We characterize the parameters that affect the approximation error, derive the upper bounds of the errors in likelihood computation and latent variable inference, and investigate the asymptotic properties of the approximate maximum likelihood estimator. We also provide a practical procedure for measuring approximation errors and selecting the number of regime periods to keep in the truncated path. All the analysis is based on our new collapsing step, which removes a nonlinear adjustment term in the existing method to facilitate theoretical derivations.