# 周辺尤度を用いたマルコフ切替モデルと確率的水準遷移モデルの比較

## 概要

This paper compares Markov switching model (Hamilton (1989)) and random level shift model (McCulloch and Tsay (1993)) using Marginal likelihood, a Bayesian model selection criteria. Markov switching (MS) model have used in many empirical analysis focusing on regime switching in economical and financial issue. On the other hand, random level shift (RLS) model have used mainly in engineering and medical statistics. But, both model can analyze some change in parameters, that is, structural change. The data made by MS model and RLS model are very similar. In economical field, analysts never know the true system. But using marginal likelihood, we can find out better model. This criteria is used in Bayesian frame work, not in classical econometrics. RLS model can not estimated by classical frame work. This model is in non-linear non-Gaussian state space model class, so, very complicated. Barnette, Kohn, Sheather and Wong (1993) show a estimation method using Bayesian Markov Chain Monte Carlo (MCMC) without approximations. Of course, for MS model, we can estimate by MCMC. First, this paper shows new estimation methods for RLS model based on MCMC. Second, we apply Chib (1995), estimate marginal likelihood of both models and compare the goodness of fit. As the result, we find out RLS model is better than MS model.