An Estimation of Regime Switching Models with Nonlinear Endogenous Switching

This paper proposes an approach to develop regime switching models where latent process determining the switching is endogenously controlled by the model shocks with free functional forms. The linear endogeneity assumption in the conventional endogenous regime switching models can therefore be relaxed. A recursive filter technique is applied to proceed maximum likelihood estimation in order to estimate the model parameters. A nonlinear endogenous two-regime switching mean-volatility model is conducted in numerical examples to investigate the model performance. In the examples, the endogeneity in switching allows heterogeneous effects of the shock signs (asymmetric endogeneity) and of the states being before the switching determination (state-dependent endogeneity). Monte Carlo simulations show that the conventional switching model ignoring the nonlinear endogeneity leads to the volatility biases. The estimates tend to be over or under their true value depending on how the endogeneity characteristics are. In particular, the true model that accounts the nonlinear endogeneity effectively provides the more precise estimates. The same model is also applied to real data of excess returns on US stock market, and the estimation results informatively describe the effects influencing the regime shifts.