Heßler Martin, Kamps Oliver
Institute for Theoretical Physics, Westphalian Wilhelms-University Münster, Wilhelm-Klemm-Straße 9 48149, North Rhine-Westphalia, Germany.
Center for Nonlinear Science, Westphalian Wilhelms-University Münster, Corrensstraße 2 48149, North Rhine-Westphalia, Germany.
PNAS Nexus. 2022 Dec 24;2(2):pgac296. doi: 10.1093/pnasnexus/pgac296. eCollection 2023 Feb.
Early warning indicators often suffer from the shortness and coarse-graining of real-world time series. Furthermore, the typically strong and correlated noise contributions in real applications are severe drawbacks for statistical measures. Even under favourable simulation conditions the measures are of limited capacity due to their qualitative nature and sometimes ambiguous trend-to-noise ratio. In order to solve these shortcomings, we analyze the stability of the system via the slope of the deterministic term of a Langevin equation, which is hypothesized to underlie the system dynamics close to the fixed point. The open-source available method is applied to a previously studied seasonal ecological model under noise levels and correlation scenarios commonly observed in real world data. We compare the results to autocorrelation, standard deviation, skewness, and kurtosis as leading indicator candidates by a Bayesian model comparison with a linear and a constant model. We show that the slope of the deterministic term is a promising alternative due to its quantitative nature and high robustness against noise levels and types. The commonly computed indicators apart from the autocorrelation with deseasonalization fail to provide reliable insights into the stability of the system in contrast to a previously performed study in which the standard deviation was found to perform best. In addition, we discuss the significant influence of the seasonal nature of the data to the robust computation of the various indicators, before we determine approximately the minimal amount of data per time window that leads to significant trends for the drift slope estimations.
早期预警指标常常受制于现实世界时间序列的短暂性和粗粒度。此外，实际应用中典型的强噪声贡献及其相关性，对于统计方法来说是严重的缺陷。即使在有利的模拟条件下，由于这些方法的定性性质以及有时模糊的趋势与噪声比，其能力也是有限的。为了解决这些缺点，我们通过朗之万方程确定性项的斜率来分析系统的稳定性，假设该方程是系统在固定点附近动力学的基础。将这种开源可用方法应用于一个先前研究过的季节性生态模型，该模型处于现实世界数据中常见的噪声水平和相关性场景下。我们通过与线性模型和常数模型的贝叶斯模型比较，将结果与自相关、标准差、偏度和峰度作为领先指标候选进行比较。我们表明，确定性项的斜率因其定量性质以及对噪声水平和类型的高稳健性，是一个很有前景的替代指标。与之前一项发现标准差表现最佳的研究相比，除了去季节化后的自相关外，通常计算的指标无法提供关于系统稳定性的可靠见解。此外，在我们确定每个时间窗口大致导致漂移斜率估计出现显著趋势所需的最少数据量之前，我们讨论了数据季节性对各种指标稳健计算的重大影响。
