TY - JOUR
T1 - Likelihood inference for dynamic linear models with Markov switching parameters
T2 - on the efficiency of the Kim filter
AU - Kim, Young Min
AU - Kang, Kyu Ho
N1 - Funding Information:
Kyu Ho Kang acknowledges financial support from the Korea University (K1709771).
PY - 2019/11/26
Y1 - 2019/11/26
N2 - 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.
AB - 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.
KW - State space model
KW - auxiliary particle filter
KW - maximum likelihood estimation
KW - posterior sampling
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U2 - 10.1080/07474938.2018.1514027
DO - 10.1080/07474938.2018.1514027
M3 - Article
AN - SCOPUS:85057342891
VL - 38
SP - 1109
EP - 1130
JO - Econometric Reviews
JF - Econometric Reviews
SN - 0747-4938
IS - 10
ER -