Several Theoretical Extensions And Applications Of Regime Switching Model

This dissertation reviews the extant work of regime switching models,and further proposes several theoretical extensions of the existing work.Specifically,this disser-tation studies the endogenous switching problem that has existed for a long time in the regime switching model,and further proposes a concept of state-varying endogene-ity.The methods of modeling,testing for and estimating state-varying endogeneity are proposed.In addition,with respect to the shortcoming of not being able to model the structural changes of panel data models with interactive fixed effects,this dissertation proposes a regime switching panel data model with interactive fixed effects.Besides,a feasible estimation method and a numerical algorithm are proposed.In Chapter 2,we propose a state-varying endogenous regime switching model?the SERS model?which includes the endogenous regime switching model by Chang et al.^[1],the CCP model,as a special case.To estimate the unknown parameters in the SERS model,we propose a maximum likelihood estimation method.Monte Carlo sim-ulation results show that in the absence of state-varying endogeneity,the SERS model and the CCP model have similar performance,while in the presence of state-varying endogeneity,the SERS model performs much better than the CCP model.Finally,we use the SERS model to analyze the China stock market returns and our empirical results show that there exists strongly state-varying endogeneity in volatility switching for the Shanghai Composite Index returns.Moreover,the SERS model can indeed produce a much more realistic assessment for regime switching process than the one obtained by the CCP model.In chapter 3,we have proposed a regime switching panel data model with in-teractive fixed effects,which substantially generalizes the existing work which either considers panel data models with interactive fixed effects but no regime switching,or panel data models with regime switching but under cross-sectional independence.We have proposed a maximum likelihood estimation method and developed an ECM?expectation and conditional maximization?algorithm to estimate the unknown param-eters.Our simulation studies have shown that the performance of the proposed method is very well.In the last chapter,we summarize our work and the possible direction for future research.