Abstract
Ever since the publication of Hamilton's (1989) seminal work on regime switching model, a large amount of its applications have been found in econometric and statistical problems. Despite its enormous popularity, one shortcoming of the model is that the model describes the regime qualitatively instead of quantitatively. In this dissertation research, we first review the classic regime switching model and its broad applications in different problems. Then we introduce a stochastic regime switching model in which the parameter in each regime is a random variable following certain distribution. A forward filtering procedure shows the posterior distribution of the parameter as a mixture distribution with explicit weights which can be calculated recursively. Furthermore, based on the reversibility of the hidden Markov chain, a backward filtering procedure can be conducted in a similar way. Based on Bayes' theorem, both the smoothing estimate of parameter and probabilities can be calculated explicitly. We also develop an expectation-maximization algorithm to estimate the hyperparameters in the model. Furthermore, we propose a bounded complexity mixture (BCMIX) approximation, which has much lower computational complexity yet comparable to the Bayes estimates in statistical efficiency. We perform intensive simulation studies to evaluate the Bayes and BCMIX estimates of time-varying parameters, in terms of the sum of squared errors, L2 errors of the estimates, the Kullback-Leibler divergence, and the identification ratios of true regimes. We also apply this model to analyze some economic time series.
