Numerical filtering of linear state-space models with Markov switching

A class of discrete-time random processes that have seen a wide variety of applications consists of a linear state-space model whose parameters are modulated by the state of a finite-state Markov chain. A typical way to filter such processes is with collapsing methods, which approximate the underlying distribution by a mixture of Gaussians indexed by the recent history of the Markov chain. The computational cost of such methods increases rapidly as the error decreases to zero. This paper presents an alternative approach to filtering these processes based on keeping track of the values of the underlying probability density function and characteristic function on grids. It has favourable convergence properties under certain assumptions.