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Estimating entropy rate from censored symbolic time series: A test for time-irreversibility
R Salgado-García1, Cesar Maldonado2
1Centro de Investigación en Ciencias-IICBA, Physics Department, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001 colonia Chamilpa, CP 62209, Cuernavaca Morelos, Mexico.
Abstract:
In this work, we introduce a method for estimating the entropy rate and the entropy production rate from a 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 the entropy rate and the 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 satisfies the central limit theorem. We test our method using a time series coming from Markov chain models, discrete-time chaotic maps, and a real DNA sequence from the human genome.
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