Kernel estimates of the mean and the volatility functions in a nonlinear autoregressive model with ARCH errors

In this paper, we deal with the nonparametric kernel estimation of the regression and volatility functions pertaining to nonlinear autoregressive model with ARCH errors. Under stationarity and ergodicity, we establish the strong uniform consistency and asymptotic normality of the estimators. Our results hold without any mixing condition and do not require the existence of marginal densities. Furthermore, rates of convergence are obtained.