Smooth Transition ARCH Models: Estimation and Testing

Abstract

In this paper, we suggest an extension of the ARCH model, the smooth-transition autoregressive conditional heteroskedasticity (STARCH) model. STARCH models endogenously allow for time-varying shifts in the parameters of the conditional variance equation. The most general form of the model that we consider is a double smooth-transition model, the STAR-STARCH model, which permits not only the conditional variance, but also the mean, to be a function of a smooth-transition term. The threshold ARCH model, the Markov-ARCH model and the standard ARCH model are special cases of our STARCH model. We also develop Lagrange multiplier tests of the hypothesis that the smooth-transition term in the conditional variance is zero. We apply our STARCH model to excess Treasury bill returns. We find some evidence of a smooth transition in excess returns, but in contrast to previous studies, we find almost no evidence of volatility persistence once we allow for smooth transitions in the conditional variance. Thus, the apparent persistence in the conditional variance reported by many researchers could be a mere statistical artifact. We conduct in-sample tests comparing STARCH models to nested competitors; these suggest that STARCH models hold promise for improved predictions. Finally, we describe further extensions of the STARCH model and suggest issues in finance to which they might profitably be applied.