量化强相关噪声下系统韧性与制度转变风险
Quantifying resilience and the risk of regime shifts under strong correlated noise
AI总结：
研究通过分析兰格方程确定性项的斜率，提出一种量化强相关噪声下系统韧性与制度转变风险的鲁棒方法。
摘要：
早期预警指标常常受到现实世界时间序列的短小和粗粒度的影响。此外，实际应用中通常较强的相关噪声贡献对统计度量是严重的缺点。即使在有利的模拟条件下，这些度量也由于其定性性质和有时模糊的趋势与噪声比而能力有限。为了解决这些不足，我们通过兰格方程确定性项的斜率分析系统的稳定性，该斜率被假设为系统动态接近固定点时的基础。该开源方法被应用于之前研究的季节生态模型，在现实世界数据中常见的噪声水平和相关性场景下进行测试。我们通过贝叶斯模型比较，使用线性和常数模型，将结果与自相关、标准差、偏度和峰度等领先指标候选者进行比较。我们证明了确定性项的斜率是一个有前景的替代方案，因为它具有定量性质和对噪声水平和类型的高鲁棒性。除了自相关去季节化外，其他常用的指标未能提供关于系统稳定性的可靠见解，与之前的一项研究形成对比，在该研究中标准差被发现表现最佳。此外，我们讨论了数据季节性对各种指标鲁棒计算的显著影响，并确定了每个时间窗口中导致漂移斜率估计显著趋势的最小数据量。
英文摘要：
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 analyse 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.
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