概要

Extension 1:

This research attempts to extend the Markov-switching model with time varying transition probabilities (TVTP). The transition probabilities in the conventional TVTP model are functions of exogenous variables that are time dependent but with constant coefficients. In this research, the coefficient parameters that express the sensitivities of the exogenous variables are also allowed to vary with time.  Since the state probabilities were nonlinear functions of the sensitivity parameters, the estimation was conducted employing the Gibbs sampling technique.

Using the data of the Japanese stock market for 34 years, the marginal likelihood values improved from the conventional MSMs by a great margin. It was also seen that the sensitivities had changed greatly through sample period and the estimated transition probabilities moved widely between 0 and 1. These results suggest that the time dependency of the sensitivities was an important factor to describe the market dynamics.

Extension 2:

In the analyses of business cycles and stock market cycles, duration dependence of the cycles has been investigated based on two different approaches. Cochrane and Defina (1995) and Zuehlke (2003, 2004) tried to formulate the hazard rates using Weibull distribution or its modified version. On the other hand, Maheu and McCurdy (2000) employed the Markov-switching model where the transition probability was expressed as a function of duration.

In the model proposed in this research, the latent variable in the transition probability is non-parametrically formulated in the state space. The empirical results of the model in the analyses of stock markets cycles and business cycles show that the actual duration dependence is not monotonic an, therefore, can be neither described by the conventional Markov-switching models nor by Weibull hazard models.