On the semi-varying coefficient dynamic panel data model with autocorrelated errors

In nonlinear time series modeling, autocorrelation of the random errors may cause critical problems in estimation and inference. The situation becomes even worse for panel data with dynamic structure. However, most of the existing literature has not taken into account this problem. The challenge comes from the fact that the expectation of random errors conditional on lag variables is hardly to be zero. Based on the extension of Whittle likelihood, a semi-parametric dynamic model with ARMA errors for panel data is proposed. Asymptotic normality for the estimators of finite parameters and varying coefficients have been established respectively. Statistical simulations show that the proposed method can efficiently remove the bias of estimation. In real data analysis, it demonstrates that the proposed method can improve prediction when errors are autocorrelated.