Time reversal symmetry and the difference between relaxations and building-up periods

Autocorrelations in stationary systems are time-symmetric, irrespective of the signal's properties. Linear dynamics is usually associated with signals which are statistically time inversion invariant. This is known to be broken for non-Gaussian models. In this paper, we develop a theoretical framework of time reversibility of linear models based on noncontinuous driving. We identify the inverse decay exponent of the autocorrelation function as either a characteristic time for the building-up of extreme events in the time series or of relaxations after these extreme events. If the characteristic time is known, the dynamics can be inverted in both directions in time and the residuals can be compared, which gives a criterion for the type of time inversion asymmetry. The method is applied to two time series from atmospheric science with different behavior.