This paper estimates a structural times series model of return volatility. We argue that the structural time series approach to GARCH modelling first suggested by Engle and Lee, has the potential to improve the empirical reliability of GARCH models, and greatly enhance their interpretability. In its structural form, our model has tow parts, a short-memory GARCH model with a time-varying benchmark variance, and a longer-memory exponential smoothing model of benchmark variance. In its reduced for, the model is equivalent to a restricted-coefficient version of the GARCH (2,2) model. We apply the model to daily equity index returns from seven countries over the period January 1980 - April 1997. The model significantly outperform unstructured GARCH in its ability to capture short, medium and long-term memory in daily return volatility.
