Successfully predicting the future states of systems that are complex, stochastic, and potentially chaotic is a major challenge. Model forecasting error (FE) is the usual measure of success; however model predictions provide no insights into the potential for improvement. In short, the realized predictability of a specific model is uninformative about whether the system is inherently predictable or whether the chosen model is a poor match for the system and our observations thereof. Ideally, model proficiency would be judged with respect to the systems’ intrinsic predictability, the highest achievable predictability given the degree to which system dynamics are the result of deterministic vs. stochastic processes. Intrinsic predictability may be quantified with permutation entropy (PE), a model‐free, information‐theoretic measure of the complexity of a time series. By means of simulations, we show that a correlation exists between estimated PE and FE and show how stochasticity, process error, and chaotic dynamics affect the relationship. This relationship is verified for a data set of 461 empirical ecological time series. We show how deviations from the expected PE–FE relationship are related to covariates of data quality and the nonlinearity of ecological dynamics. These results demonstrate a theoretically grounded basis for a model‐free evaluation of a system's intrinsic predictability. Identifying the gap between the intrinsic and realized predictability of time series will enable researchers to understand whether forecasting proficiency is limited by the quality and quantity of their data or the ability of the chosen forecasting model to explain the data. Intrinsic predictability also provides a model‐free baseline of forecasting proficiency against which modeling efforts can be evaluated.

中文翻译：

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生态时间序列的内在可预测性及其指导预报的潜力

成功地预测复杂，随机且可能混乱的系统的未来状态是一项重大挑战。模型预测误差（FE）是成功的常用指标；但是，模型预测无法提供改进潜力的见解。简而言之，特定模型的已实现的可预测性对于系统是否固有可预测或所选择的模型是否与系统及其观察结果的匹配性不足。理想情况下，应根据系统的固有能力来判断模型熟练程度可预测性，因为系统动力学是确定性过程与随机过程的结果，因此可达到的最高可预测性。内在可预测性可以用置换熵（PE）进行量化，置换熵是对时间序列复杂性的无模型，信息论的度量。通过仿真，我们表明估计的PE和FE之间存在相关性，并表明随机性，过程误差和混沌动力学如何影响这种关系。对于461个经验生态时间序列的数据集，已验证了这种关系。我们展示了与预期的PE-FE关系的偏离如何与数据质量的协变量和生态动力学的非线性相关。这些结果证明了对系统内在可预测性进行无模型评估的理论基础。识别时间序列的内在和实现的可预测性之间的差距将使研究人员能够了解预测熟练程度是否受到其数据的质量和数量的限制，还是受所选预测模型解释数据的能力的限制。本征可预测性还提供了预测能力的无模型基线，可以根据该基线评估建模工作。