Switching state-space models - Likelihood function, filtering and smoothing

In this paper we consider the joint modeling of an observable time series y(t) and of an unobservable process s(t), capturing possible changes of regime, when (y(t),s(t)) is not necessarily jointly Markovian. For instance, models with moving-average components in the switching regime models, for which Hamilton's algorithm fails, are particular cases. We introduce a general switching state-space model and, in this framework, we propose a combination of the partial Kalman filter and of importance sampling techniques in order to compute the likelihood function. Moreover, various variance-reductions methods based on sequentially optimal approaches are given. These approaches are computationally simpler if s(t) is a qualitative variable, i.e. it takes only a finite number of values, and in this setting Monte Carlo studies show the practical feasibility and the efficiency of the methods proposed. The filtering and smoothing problems are also dealt with. (C) 1998 Elsevier Science B.V. All rights reserved.