Economists continue to debate the importance of nonlinearity to their discipline. When it comes to forecasting levels, unit roots seems to be quite prevalent, and there has been a great deal of skepticism about nonlinear models. See the arguments pro and con in Ramsey (1996). The time series properties of higher moments have, however, led researchers to go beyond the standard linear, normally distributed world of the textbooks. The two most widely developed lines of research in this area are the ARCH volatility models of Engle (1982), and the asymmetric Markov-switching model of Hamilton (1989). Our focus in this paper concerns numerical procedures for the estimation of the MS type of models.