The BLHK Filter

An important task associated with the statistical analysis of MS-VAR models is discussed in this chapter: the filtering and smoothing of regime probabilities. In the MS-VAR model the state vector ξ _t is given a structural interpretation. Thus an inference on this unobserved variable is of interest for its own sake. However, the filtered and smoothed state probabilities provide not only information about the regime at time t, but also open the way for the computation of the likelihood function and consequently for maximum likelihood estimation and likelihood ratio tests.