Saddlepoint approximation methods for testing of serial correlation in panel time series data

Abstract

The saddlepoint method is used to approximate the tail probabilities of the lag one serial correlation coefficient α, of a zero mean, first-order auto-regressive process, for both large and small numbers of small samples, and to test for serial correlation in a first-order non-zero mean process. The formula for the tail probability due to Lugannani and Rice is extended to the current problem. In the case of the zero mean process, approximate tail probabilities are computed using our results, and are compared with the Edgeworth and normal approximations. Unlike the other two approximations, the saddlepoint approximation performs uniformly well over the whole range of tail probability values considered. For the testing of serial correlation in the non-zero mean process, the saddlepoint method used to obtain the P-values performs in a similar manner to the asymptotic normal approximation method used by Cox and Solomon [Cox, D.R. and Solomon, P.J. (1988). On testing for serial correlation in large numbers of small samples. Biometrika, 75, 145–148].