Unobservable Markov Chain Research Articles

Bayesian Analysis of a Two-State Markov Modulated Poisson Process

We postulate observations from a Poisson process whose rate parameter modulates between two values determined by an unobserved Markov chain. The theory switches from continuous to discrete time by considering the intervals between observations as a sequence of dependent random variables. A result from hidden Markov models allows us to sample from the posterior distribution of the model parameters given the observed event times using a Gibbs sampler with only two steps per iteration.

COINTEGRATION AND CHANGES IN REGIME: THE JAPANESE CONSUMPTION FUNCTION

In this paper we examine a model of cointegration where long-run parameters are subject to switching between several different cointegrating regimes. These shifts are allowed to be governed by the outcome of an unobserved Markov chain with unknown transition probabilities. We illustrate this approach using Japanese data on consumption and disposable income, and find that the data favour a Markov-switching long-run relationship over a standard temporally stable formulation. © 1997 by John Wiley & Sons, Ltd.

Autoregressive conditional heteroskedasticity and changes in regime

ARCH models often impute a lot of persistence to stock volatility and yet give relatively poor forecasts. One explanation is that extremely large shocks, such as the October 1987 crash, arise from quite different causes and have different consequences for subsequent volatility than do small shocks. We explore this possibility with U.S. weekly stock returns, allowing the parameters of an ARCH process to come from one of several different regimes, with transitions between regimes governed by an unobserved Markov chain. We estimate models with two to four regimes in which the latent innovations come from Gaussian and Student t distributions.