Asymptotic normality for the weighted estimators in heteroscedastic partially linear regression model under dependent errors

Abstract

In this article, we investigate the estimators for the heteroscadastic partially linear regression model under dependent errors defined by y i = x i β + g ( t i ) + ε i ( 1 ≤ i ≤ n ) , where ε i = σ i e i , σ i 2 = f ( u i ) , the design points ( x i , t i , u i ) are known and nonrandom, β is an unknown parameter to be estimated, the functions g(⋅) and f(⋅) are unknown, which are defined on a closed interval [0,1], and the random errors {e i } are (α, β)-mixing random variables. When the model is heteroscedastic, the unknown parameter β and the unknown function g(⋅) are approximated by the weighted least squares estimators. We derive the asymptotic normality of the weighted least squares estimators under some suitable conditions. Simulation studies are conducted to demonstrate the finite sample performance of the proposed procedure. Finally, we use real data to examine the dependence between oil prices and exchange rates.