Estimating entropy rate from censored symbolic time series: a test for time-irreversibility
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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 this is a parameter of a (limiting) distribution. The last statement is actually a consequence of the fact that the distribution of estimators coming from recurrence-time statistics comply with the central limit theorem. We test our method in a Markov chain model where these quantities can be exactly computed.
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