Inferring intrinsic predictability (IP) or predictability limit (PL) from time series plays a crucial role in understanding complex systems and guiding predictions. Though PL is often considered to depend on the characteristic timescale (CT) of an underlying process, the quantitative relation between IP, PL and CT has not been well studied. As the simplest process with an adjustable CT, the Auto-Regression of order one, i.e. AR(1), is taken as a representative process to explore this quantitative relation, then this relation is leveraged to estimate PL. Our results show that directly estimating the PL highly relies on the CT of a specific AR(1) process, and the uncertainties and bias of PL estimations dramatically increase with the enhanced CT, which indicates that more data points and computational cost are required for reliably estimating PL from the process with a large CT value, and it is unrealizable to directly estimate PL from most of real-world series with limited length. To solve this problem, an IP metric, i.e. the time series predictability defined by the weighted permutation entropy (WPE), is proposed to indirectly estimate PL reliably with much lower uncertainties without biases for short series. The findings in this study can greatly improve the accuracy of PL estimation and in-depth understandings on the predictability studies.

从时间序列推断内在可预测性（IP）或可预测性极限（PL）对于理解复杂系统和指导预测起着至关重要的作用。尽管 PL 通常被认为取决于底层过程的特征时间尺度 (CT)，但 IP、PL 和 CT 之间的定量关系尚未得到很好的研究。作为最简单的可调节 CT 过程，以一阶自回归，即 AR(1)，作为代表性过程来探索这种定量关系，然后利用这种关系来估计 PL。我们的结果表明，直接估计 PL 高度依赖于特定 AR(1) 过程的 CT，并且 PL 估计的不确定性和偏差随着 CT 的增强而急剧增加，这表明需要更多的数据点和计算成本才能可靠地估计 PL。从具有大CT值的过程中估计PL，并且从大多数长度有限的现实世界序列中直接估计PL是无法实现的。为了解决这个问题，提出了一种IP度量，即由加权排列熵（WPE）定义的时间序列可预测性，以低得多的不确定性间接可靠地估计PL，并且不会对短序列产生偏差。本研究的结果可以极大地提高PL估计的准确性和对可预测性研究的深入理解。