Testing for Error Correlation in Semi-Functional Linear Models

Existing methods for analyzing semi-functional linear models usually assumed that random errors are not serially correlated or serially correlated with the known order. However, in some applications, these assumptions on random errors may be unreasonable or questionable. To this end, this paper aims at testing error correlation in a semi-functional linear model (SFLM). Based on the empirical likelihood approach, the authors construct an empirical likelihood ratio statistic to test the serial correlation of random errors and identify the order of autocorrelation if the serial correlation holds. The proposed test statistic does not need to estimate the variance as it is data adaptive and possesses the nonparametric version of Wilks' theorem. Simulation studies are conducted to investigate the performance of the proposed test procedure. Two real examples are illustrated by the proposed test method.