EFFICIENT ESTIMATION IN SEMIPARAMETRIC GARCH MODELS

It is well-known that financial data sets exhibit conditional heterosk edasticity. GARCH-type models are often used to model this phenomenon, Since the distribution of the rescaled innovations is generally far f rom a normal distribution, a semiparametric approach is advisable. Sev eral publications observed that adaptive estimation of the Euclidean p arameters is not possible in the usual parametrization when the distri bution of the rescaled innovations is the unknown nuisance parameter, However, there exists a reparametrization such that the efficient scor e functions in the parametric model of the autoregression parameters a re orthogonal to the tangent space generated by the nuisance parameter , thus suggesting that adaptive estimation of the autoregression param eters is possible, Indeed, we construct adaptive and hence efficient e stimators in a general GARCH in mean-type context including integrated GARCH models, Our analysis is based on a general LAN theorem for time -series models, published elsewhere, In contrast to recent literature about ARCH models we do not need any moment condition. (C) 1997 Elsevi er Science S.A.