Centro de Investigación en Ciencias-IICBA, Physics Department, Universidad Autónoma del Estado de Morelos, Avenida Universidad 1001 colonia Chamilpa, CP 62209, Cuernavaca Morelos, Mexico.
IPICYT/División de Control y Sistemas Dinámicos, Camino a la Presa San José 2055, Lomas 4a. sección, C.P. 78216, San Luis Potosí, S.L.P., Mexico.
Chaos. 2021 Jan;31(1):013131. doi: 10.1063/5.0032515.
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.
在这项工作中，我们介绍了一种从有限符号时间序列估计熵率和熵产生率的方法。从统计学的角度来看，从有限序列中估计熵可以解释为估计具有截尾或截断样本的分布参数的问题。我们使用这一观点来给出熵率和熵产生率的估计，假设它们是（极限）分布的参数。最后一个陈述实际上是由这样一个事实所导致的，即从递归时间统计中得到的估计分布满足中心极限定理。我们使用来自马尔可夫链模型、离散时间混沌映射和人类基因组中真实 DNA 序列的时间序列来测试我们的方法。
