Imposing stationarity constraints on the parameters of ARCH and GARCH models

In their seminal papers on ARCH and GARCH models, Engle (1982) and Bollerslev (1986) specified parametric inequality constraints that were sufficient for non-negativity and weak stationarity of the estimated conditional variance function. This paper uses Bayesian methodology to impose these constraints on the parameters of an ARCH(3) and a GARCH(1,1) model. The two models are used to explain volatility in the London Metals Exchange Index. Model uncertainty is resolved using Bayesian model averaging. Results include estimated posterior pdfs for one-step-ahead conditional variance forecasts.