Test for the covariance matrix in time-varying coefficients panel data models with fixed effects

This paper proposes tests for the null of sphericity and identity matrix for nonparametric time-varying coefficient panel data models with fixed effects. Firstly, based on the local linear smoothing technique, the estimators of the unknown coefficient functions and model residuals are obtained. Secondly, proper test statistics are proposed aiming at tests for sphericity or identity matrix with a large number of cross-sectional units and time series observations. In addition, the limiting distributions of the proposed test statistics are derived based on random matrix theory. At last, some simulation studies are conducted to examine the finite sample performance for the proposed test statistics and a real data example is analyzed.