Nonparametric estimation of the conditional variance function with correlated errors

In this paper, we consider a fixed regression model where the errors are a strictly stationary process and in which both functions, the conditional mean and the conditional variance (volatility), are unknown. Two nonparametric estimators of the volatility function based on local polynomial fitting are studied. Expressions of the asymptotic bias and variance are given and the asymptotic normality is shown for both estimators. The influence of the dependence of the data is observed in the expressions of the variance. A simulation study and an analysis with real economic data illustrate the behavior of the proposed nonparametric estimators.