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

TL;DR

This paper presents a novel method for estimating entropy rate and entropy production rate from finite symbolic time series, applicable to various data types including biological sequences, by treating the problem as parameter estimation of a distribution.

Contribution

It introduces a new statistical approach to estimate entropy rates from censored symbolic data, leveraging the central limit theorem for improved accuracy.

Findings

Method accurately estimates entropy rate in Markov and chaotic models

Effective in analyzing real DNA sequences for entropy production

Provides a statistical framework for entropy estimation from finite data

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.