Symbolic approach for measuring temporal “irreversibility”

Abstract

We describe a symbolic approach for measuring temporal "irreversibility" in time-series measurements. Temporal irreversibility is important because it excludes Gaussian linear dynamics and static transformations of such dynamics from the set of possible generating processes. A symbolic method for measuring temporal irreversibility is attractive because it is computationally efficient, robust to noise, and simplifies statistical analysis of confidence limits. We propose a specific algorithm, called "false flipped symbols," for establishing the presence of temporal irreversibility without the need for generating surrogate data. Besides characterizing experimental data, our results are relevant to the question of selecting alternative models. We illustrate our points with numerical model output and experimental measurements.

Ictal time-irreversible intracranial EEG signals as markers of the epileptogenic zone

“…This is observed, for example, in signals with uneven slopes of their rising and falling parts (or "phases" to use the vocabulary of visual EEG interpretation). In the language of quantitative signal analysis, one refers to this feature as time-irreversibility, which means that statistical properties are different depending on whether a signal is analysed forward or backward in time (Daw et al, 2000). The importance of this asymmetry as a characteristic of epileptiform signals has long been known to epileptologists, even being illustrated almost forty years ago by Gloor in a seminal book chapter (see Figure 1 in Gloor's publication) about the use of EEG in the differential diagnosis of epilepsy (Gloor, 1977).…”

Detecting nonlinearity in time series driven by non-Gaussian noise: the case of river flows

“…For example, the time series in Fig. 1a exhibits a clear temporal irreversibility, that contrasts with the reversibility characteristic of linear Gaussian processes (Weiss, 1975;Diks et al, 1995;Daw et al, 2000). In fact, the simple third order statistic r proposed by Schreiber and Schmitz (2000) to test for reversibility produces a value of r=0.34 for the linear shot noise process, well above the maximum value of r=0.095 obtained from 20 surrogate series.…”

Symbolic Time Series Analysis and Its Application in Social Sciences

“…Mechanical systems were one of the first applications where symbolic analysis was successfully used to characterize complex dynamics. In [24][25][26], symbolic methods to the analysis of experimental combustion data from internal combustion engines are applied. Their objective was to study the onset of combustion instabilities as the fueling mixture was leaned.…”