Likelihood inference for dynamic linear models with Markov switching parameters: on the efficiency of the Kim filter

Abstract

The Kim filter (KF) approximation is widely used for the likelihood calculation of dynamic linear models with Markov regime-switching parameters. However, despite its popularity, its approximation error has not yet been examined rigorously. Therefore, this study investigates the reliability of the KF approximation for maximum likelihood (ML) and Bayesian estimations. To measure the approximation error, we compare the outcomes of the KF method with those of the auxiliary particle filter (APF). The APF is a numerical method that requires a longer computing time, but its numerical error can be sufficiently minimized by increasing simulation size. According to our extensive simulation and empirical studies, the likelihood values obtained from the KF approximation are practically identical to those of the APF. Furthermore, we show that the KF method is reliable, particularly when regimes are persistent and sample size is small. From the Bayesian perspective, we show that the KF method improves the efficiency of posterior simulation. This study contributes to the literature by providing evidence to justify the use of the KF method in both ML and Bayesian estimations.