A versatile and robust metric entropy test of time-reversibility, and other hypotheses

We examine the performance of a metric entropy statistic as a robust test for time-reversibility (TR), symmetry, and serial dependence. It also serves as a measure of goodness-of-fit. The statistic provides a consistent and unified basis in model search, and is a powerful diagnostic measure with surprising ability to pinpoint areas of model failure. We provide empirical evidence comparing the performance of the proposed procedure with some of the modern competitors in nonlinear time-series analysis, such as robust implementations of the BDS and characteristic function-based tests of TR, along with correlation-based competitors such as the Ljung–Box Q-statistic. Unlike our procedure, each of its competitors is motivated for a different, specific, context and hypothesis. Our evidence is based on Monte Carlo simulations along with an application to several stock indices for the US equity market.