Assessing Time-Reversibility Under Minimal Assumptions

This article considers a simple procedure for assessing whether a weakly dependent univariate stochastic process is time-reversible. Our approach is based on a simple index of the deviation from zero of the median of the one-dimensional marginal law of differenced data. An attractive feature of the method is that it requires no moment assumptions. Instead of relying on Gaussian asymptotic approximations, we consider using subsampling and resampling methods to construct confidence intervals for the time-reversibility parameter, and show that such inference procedures are asymptotically valid under a mild mixing condition. The small-sample properties of the proposed procedures are examined by means of Monte Carlo experiments and an application to real-world data is also presented. Copyright 2008 The Author. Journal compilation 2008 Blackwell Publishing Ltd