On Nonparametric Estimation of a Nonparametric Autoregressive Conditionally Heteroscedastic Process

Since the studies of Engel (1982) and Bollerslev (1986), the ARCH and GARCH processes have been used extensively to model volatile series. However, Pagan and Schwert (1990) have shown the limits of these choices. This deficiency is overcome by the NonParametric AutoRegressive Conditionally Heteroscedastic (NPARCH) processes. In this work, we use the Nadaraya-Watson method to estimate the autoregression and volatility functions of a NPARCH process. We show the strong consistency and the asymptotic normality of these estimators. Through brief simulations, we illustrate these two properties.