Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality

We consider the estimation and identification of the functional structures of nonlinear econometric systems of the ARCH type. We employ nonparametric kernel estimates for the nonlinear functions characterizing the systems, and we establish strong consistency along with sharp rates of convergence under mild regularity conditions. We also prove the asymptotic normality of the estimates.