标题： 熵与复杂度的联合渐近分布 显示英文标题

标题： The Joint Asymptotic Distribution of Entropy and Complexity

摘要： 我们在弱依赖条件下推导了有序模式频率的渐近分布，并不仅通过分析方法研究了移动平均、高斯和新型广义抛硬币过程的长期协方差矩阵，还通过基于模拟的方法进行了近似研究。 然后，我们推导了熵-复杂度对的渐近分布，该对已成为总结时间序列动态的流行工具。 在此，我们区分了均匀和非均匀的有序模式分布，并因此得到了两个不同的极限定理。 在此基础上，我们考虑了一个序列依赖检验并检查了其小样本性能。 此外，我们利用渐近结果来近似熵-复杂度对的估计不确定性。 显示英文摘要

摘要： We derive the asymptotic distribution of ordinal-pattern frequencies under weak dependence conditions and investigate the long-run covariance matrix not only analytically for moving-average, Gaussian, and the novel generalized coin-tossing processes, but also approximately by a simulation-based approach. Then, we deduce the asymptotic distribution of the entropy-complexity pair, which emerged as a popular tool for summarizing the time-series dynamics. Here, we make the necessary distinction between a uniform and a non-uniform ordinal pattern distribution and, thus, obtain two different limit theorems. On this basis, we consider a test for serial dependence and check its finite-sample performance. Moreover, we use our asymptotic results to approximate the estimation uncertainty of entropy-complexity pairs.