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.