Testing Serial Correlation in Semiparametric Time Series Models

Abstract

Abstract. In this paper, we propose two test statistics for testing serial correlation in semiparametric time series model that could allow lagged dependent variables as explanatory variables. The first one is testing for zero first‐order serial correlation and the second is for testing higher‐order serial correlation. The test statistics are shown to have asymptotic normal or χ 2 distributions under the assumption of a martingale difference error process. Our results generalize some of the test statistics of Li and Hsiao (1998 ), that were developed for the case of panel data with a large N and a fixed T , to the case of a large T with N either small or large.