Nonparametric Autoregression with Multiplicative Volatility and Additive Mean

For over a decade nonparametric modelling has been successfully applied to study nonlinear structures in nancial time series It is well known that the usual nonpara metric models often have less than satisfactory performance when dealing with more than one lag When the mean has an additive structure however better estimation methods are available which fully exploit such a structure Although in the past such nonparametric applications had been focused more on the estimation of the conditional mean it is equally if not more important to measure the future risk of the series along with the mean For the volatility function i e the conditional variance given the past a multiplicative structure is more appropriate than an additive one as the volatility is a positive scale function and a multiplicative model provides a better interpretation of each lagged value s in uence on such a function In this paper we consider the joint estimation of both the additive mean and the multiplicative volatility The technique used is marginally integrated local polynomial estimation The procedure is applied to the DEM USD Deutsche Mark US Dollar daily exchange returns Acknowledgements This research was nancially supported by Sonderforschungsbereich Quan ti kation und Simulation Okonomischer Prozesse Deutsche Forschungsgemeinschaft at Humboldt Univer sit at zu Berlin We appreciate the interests of our colleagues that motivated our work especially Christian Hafner Helmut L utkepohl and Rolf Tschernig We have also bene ted from the elegant formulation of the marginal integration technique by Eric Severance Lossin and Stefan Sperlich Finally we want to thank the two anonymous referees who gave us many constructive comments