Some Statistic Models And Analysis For First-Order Nonparametric Autoregressive Errors

The regressive model with dependent error terms is the important problem for financial time series and economics. But we should notice that: the regressive model with linear dependent error can't reflect the nonlinear character, and nonlinear dependent error model makes the modeling lost the agility, such as ARCH and GARCH model, and so on. Nonparametric method is the hotspot problem for nonparametric modeling.In this paper, we mostly investigate and analyze the three statistic models for first order nonparametric auto regression error, such as: linear regression model, nonparametric regression model and semi nonparametric regression model. We obtain several results as follows:1. For the linear regression model in first-order nonparametric auto regression error, under random-design, local linear estimation of parameter and nonparametric function are studied, and proved the asymptotic normal property of the parametric estimation, simultaneity giving the convergence rate of nonparametric function estimation. The simulated experiment shows local linear method works quite well.2. For the nonparametric regression model in first-order nonparametric auto regression error, under fixed-design, the kernel estimation of regressive function and error's regressive function are studied, and proved the asymptotic normal property of the estimators. The simulated experiment shows kernel method works quite well.3. For the semi nonparametric regression model in first-order nonparametric auto regression error, under fixed-design, the kernel estimation of the parameter and nonparametric function are studied, and proved the asymptotic normal property and the strong congruence.