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Nonparametric estimation of the conditional variance function with correlated errors. (English) Zbl 1106.62048
Summary: 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 nonparamerric 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 obsersed in the expressions of the variance. A simulation study and an analysis with real economic data illustrate the behavior of the proposed nonparametric estimators.

MSC:
62G08 Nonparametric regression and quantile regression
62G20 Asymptotic properties of nonparametric inference
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62P05 Applications of statistics to actuarial sciences and financial mathematics
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