Abstract: In this paper, we consider a panel data varying-coefficient partially linear model errors correlated in space and time. A serially correlated error structure is adopted for the correlation in time, and we propose an estimating procedure for the autoregressive coefficients in our set-up by combining a polynomial spline series approximation with least squares. The resulted estimators are shown to enjoy asymptotic properties. We construct a weighted semiparametric least squares estimator (WSLSE) and a weighted polynomial spline series estimator (WPSSE) for the parametric and nonparametric components of the mean model, respectively. The WSLSE is shown to be asymptotically normal and more efficient than the unweighted one, and the WPSSE is shown to achieve the optimal nonparametric convergence rate. Some simulation studies are reported to illustrate the finite sample performance of the proposed procedure. An application to Indonesian rice farming data is given.

Key words and phrases: Asymptotic normality, panel data, partially linear varying coefficient model, spatial, time-wise correlation.