A further extension of duration-dependent models

The duration dependence of stock market cycles has been investigated using the Markov switching model where the market conditions are unobservable. In conventional modeling, restrictions are imposed such that the transition probability is a monotonic function of duration, which is truncated at a certain value. This paper proposes a model that is free from these arbitrary restrictions and nests the conventional models. In the model, the parameters that characterize the transition probability are formulated in the state space. Empirical results from several stock markets show that the duration structures greatly differ depending on countries. These structures are not necessarily monotonic functions of duration and, therefore, cannot be described by the conventional models.