  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.
