标题： 时间序列高阶时间相关性的自相关函数分析：一个指数情形 显示英文标题

标题： Analysis of the autocorrelation function for time series with higher-order temporal correlations: An exponential case

摘要： 时间序列中观察到的时序相关性已通过自相关函数进行了表征。 这种相关性可以通过重尾事件间隔时间分布以及事件间隔时间之间的相关性来解释。 后者被称为高阶时序相关性，它们通过“爆发”的概念被捕捉到；爆发表示在短时间内迅速发生的一组连续事件，并且与其他爆发之间由长时间间隔分隔。 爆发中的事件数量称为爆发大小。 一些实证分析表明，连续的爆发大小彼此相关。 为了研究这种相关性对自相关函数的影响，我们设计了一个模型，通过采用Copula方法生成具有高阶时序相关性的时序数据。 我们成功地推导了当连续爆发大小相关时，该模型时序数据的自相关函数的解析解，适用于任意的事件间隔时间和爆发大小分布。 为了演示我们的分析，我们采用了事件间隔时间和爆发大小的指数分布，以了解连续爆发大小之间的相关性如何影响自相关函数的衰减行为。 显示英文摘要

摘要： Temporal correlations in the time series observed in various systems have been characterized by the autocorrelation function. Such correlations can be explained by heavy-tailed interevent time distributions as well as by correlations between interevent times. The latter is called higher-order temporal correlations, and they have been captured by the notion of bursts; a burst indicates a set of consecutive events that rapidly occur within a short time period and are separated from other bursts by long time intervals. The number of events in the burst is called a burst size. Some empirical analyses have shown that consecutive burst sizes are correlated with each other. To study the impact of such correlations on the autocorrelation function, we devise a model generating a time series with higher-order temporal correlations by employing the copula method. We successfully derive the analytical solution of the autocorrelation function of the model time series for arbitrary distributions of interevent times and burst sizes when consecutive burst sizes are correlated. For the demonstration of our analysis, we adopt exponential distributions of interevent times and burst sizes to understand how the correlations between consecutive burst sizes affect the decaying behavior of the autocorrelation function.