ASYMPTOTIC FILTERING THEORY FOR MULTIVARIATE ARCH MODELS

ARCH models are widely used to estimate conditional variances and cova riances in financial time series models. How successfully can ARCH mod els carry out this estimation when they are misspecified? How can ARCH models be made robust to misspecification? Nelson and Foster (1994a) employed continuous record asymptotics to answer these questions in th e univariate case. This paper considers the general multivariate case. Our results allow us, for example, to construct an asymptotically opt imal ARCH model for estimating the conditional variance or conditional beta of a stock return given lagged returns on the stock, volume, mar ket returns, implicit volatility from options contracts, and other rel evant data. We also allow for time-varying shapes of conditional densi ties (e.g., 'heteroskewticity' and 'heterokurticity'). Examples are pr ovided.