Local Estimation in AR Models with Nonparametric ARCH Errors

Abstract

In this article, we consider the problem of estimating the volatility function of a parametric AR(1) model with nonparametric ARCH(1) errors. Consistency and asymptotic normality of local constant and local log-linear estimators are established. Our simulation study and an application to finance lead to superior performance of the local log-linear estimator compared with the conventional treatments in the literature. A possible extension of the estimation procedure is described.