Time Reversibility statistic
timeAsymmetry(time.series)The time simmetry statistic.
The time series used to compute the statistic.
Constantino A. Garcia
The time simmetry statistic measures the asymmetry of a time series under time reversal by calculating: $$E[s_n\cdot s_{n+1}^2] - E[s_n^2\cdot s_{n+1}] $$. Since linear stochastic series are symmetric under time reversal, this statistic may be used for testing the assertion that the data was generated from a stationary linear stochastic process or not.
H. Kantz and T. Schreiber: Nonlinear Time series Analysis (Cambridge university press, second edition, section 7.1.3)