Adaptive filtering for GARCH models

Abstract

The volatility of a speculative asset is a fundamental ingredient of many financial pricing algorithms, therefore, accurate forecasts of volatility are essential to financial practioners. Autoregressive Conditional Heteroscekdastic models and their generalisations (GARCH) have been shown to provide reasonable forecasts of volatility with relatively few parameters. Recent evidence suggests, however, that financial volatility is a multiplicative process whereby dominant time frames can be located by the derivative of volatility [14]. Using the Widrow Hoff learning rule, this paper shows how the GARCH(1,1) forecast can be improved by filtering the volatility derivative against the residual forecast error from a GARCH(1,1) model. Information criterion is used to evaluate the contribution of the new adaptive parameter.