Robust modelling of ARCH models

The autoregressive conditional heteroscedastic (ARCH) model and its extensi ons have been widely used in modelling changing variances in financial time series. Since the asset return distributions frequently display tails heav ier than normal distributions, it is worth while studying robust ARCH model ling without a specific distribution assumption. In this paper, rather than modelling the conditional variance, we study ARCH modelling for the condit ional scale. We examine the L-1-estimation of ARCH models and derive the li miting distributions oi. the estimators. A robust standardized absolute res idual autocorrelation based on least absolute deviation estimation is propo sed. Then a robust portmanteau statistic is constructed to test the adequac y of the model, especially the specification of the conditional scale. We o btain their asymptotic distributions under mild conditions. Examples show t hat the suggested L-1-norm estimators and the goodness-of-fit test are robu st against error distributions and are accurate for moderate sample sizes. This paper provides a useful tool in modelling conditional heteroscedastic time series data. Copyright (C) 2001 John Wiley & Sons, Ltd.