Testing Serial Independence against Time Irreversibility

In this paper we propose a unified framework for testing serial independence against time irreversibility. This framework extends the time reversibility tests of Ramsey and Rothman(1996, Journal of Money, Credit and Banking) and Chen, Chou, and Kuan(2000,Journal of Econometrics) in several important directions. It consists of a pair of original-series-based individual and portmanteau tests and the corresponding model diagnostic checks. The former can be used to detect asymmetries in time series, and the latter can be applied to check if such asymmetries are properly explained by an econometric model. A Monte Carlo simulation shows that the proposed tests perform suitably in finite samples. An empirical example further shows that the proposed method is a useful complement to the conventional independence tests for checking the adequacy of different GARCH models.