Wavelet Methods Of Heteroscedastic Time Series Models With Trend Component

The wavelet has good local properties.The wavelet method is used to discuss the heteroscedastic time series models with trend component,so that the wavelet estimation theories of nonparametric regression models can be perfected.In order to explore the wavelet estimation and asymptotic theories of the heteroscedasticity time series models with trend component under fixed design,the linear trend and nonparametric trend with different dependent errors are considered in this paper.The main contents and conclusions are as follows:For the heteroscedastic time series models with linear trend,the weighted least square estimation based on the wavelet method is used to construct the weighted wavelet estimators of the parameters and variance function.Under the?α-mixing errors,the asymptotic normality and weak convergence rates of the parameter wavelet estimators and the weak convergence rate of the wavelet estimator of the variance function are obtained by some mathematical tools such as Cauchy inequality and Chebyshev inequality.For the heteroscedasticity time series models with nonparametric trend,the wavelet estimators of nonparametric regression function and variance function are constructed.When the random errors {ε_i } are the linear process,and random variables?{z_i}?that construct the linear errors?{ε_i}?are independent identical distribution,the weak convergence rates of the wavelet estimators of the nonparametric regression function and the variance function are obtained.Under the appropriate conditions,the weak convergence rates of wavelet estimators of nonparametric regression function and variance function are the same.Furthermore,for the heteroscedasticity time series models with nonparametric trend,the random variables {z_i}?in the linear process errors{ε_i} are extended to be the φ-mixing.Under the wild condition,the weak convergence rates of the wavelet estimators of the nonparametric regression function and the variance function are obtained.