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Testing time symmetry in time series using data compression dictionaries.

Matthew B Kennel¹

¹Institute For Nonlinear Science, University of California, San Diego, La Jolla, California 92093-0402, USA. mkennel@ucsd.edu

Physical Review. E, Statistical, Nonlinear, and Soft Matter Physics

|July 13, 2004

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This study introduces a novel method to detect time symmetry in dynamical systems using symbolic dynamics and data compression. The technique effectively distinguishes reversible processes from irreversible ones in time-series data.

Area of Science:

Dynamical Systems Theory
Statistical Physics
Information Theory

Background:

Statistical time reversibility is a property where time-series segments and their reversals have equal probability.
Linear stochastic Gaussian processes are typically reversible, while nonlinear dynamics like dissipative chaos are often irreversible.
Distinguishing between these classes of processes is crucial for understanding complex systems.

Purpose of the Study:

To develop a robust statistical test for time symmetry in dynamical processes.
To differentiate between time-reversible and time-irreversible systems from observed time-series data.
To adapt the test to arbitrary dynamics with unknown time correlations.

Main Methods:

Symbolic dynamics is employed to represent the time series.

Related Experiment Videos

Adaptive dictionary data compression algorithms are utilized to estimate reversibility.

A likelihood test is formulated based on data compression principles.

The method allows for a direct null test without resampling or surrogate data.

Main Results:

The proposed technique successfully distinguishes between time-reversible and time-irreversible systems.
Demonstrated effectiveness on diverse time-series data from both reversible and irreversible systems.
The method provides a general-purpose and robust statistical procedure.

Conclusions:

The symbolic dynamics and data compression approach offers an effective tool for assessing time symmetry.
This method can separate distinct classes of dynamical hypotheses based on time-series observations.
The technique is applicable to a wide range of complex systems with unknown dynamics.