Estimating entropy rate from censored symbolic time series: a test for time-irreversibility

Abstract

In this work we introduce a method for estimating entropy rate and entropy production rate from finite symbolic time series. From the point of view of statistics, estimating entropy from a finite series can be interpreted as a problem of estimating parameters of a distribution with a censored or truncated sample. We use this point of view to give estimations of entropy rate and entropy production rate assuming that they are parameters of a (limit) distribution. The last statement is actually a consequence of the fact that the distribution of estimations obtained from recurrence-time statistics satisfy the central limit theorem. We test our method using time series coming from Markov chain models, discrete-time chaotic maps and real a DNA sequence from human genome.

arXiv comment17 pages, 14 figures, 6 tables

References in corpus (16)

• The Fluctuation Theorem as a Gibbs Property
• Entropy estimation of symbol sequences
• Time series irreversibility: a visibility graph approach
• Kolmogorov-Sinai entropy-rate vs. physical entropy
• Entropy production and Kullback-Leibler divergence between stationary trajectories of discrete systems
• Entropy estimates of small data sets
• Fluctuations in Nonequilibrium Statistical Mechanics: Models, Mathematical Theory, Physical Mechanisms
• Time reversibility from visibility graphs of non-stationary processes
• Sharp error terms for return time statistics under mixing conditions
• DNA viewed as an out-of-equilibrium structure
• The arrow of time across five centuries of classical music
• A note on entropy estimation
• Testing the irreversibility of a Gibbsian process via hitting and return times
• Concentration bounds for entropy estimation of one-dimensional Gibbs measures
• Noise-induced rectification in out-of-equilibrium structures
• Symbolic Complexity for Nucleotide Sequences: A Sign of the Genome Structure

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• Irreversibility of symbolic time series: a cautionary tale