Detecting early warning signals in climatic time series is essential for anticipating critical transitions and tipping points. Common statistical indicators include increased variance and lag-one autocorrelation prior to bifurcation points. However, these indicators are sensitive to observational noise, long-term mean trends, and long-memory dependence, all of which are prevalent in climatic time series. Such effects can easily obscure genuine signals or generate spurious detections. To address these challenges, we employ a flexible Bayesian framework for modelling time-varying autocorrelation in long-range dependent time series, also accounting for time-varying variance. The approach uses a mixture of two fractional Gaussian noise processes with a time-dependent weight function to represent fractional Gaussian noise with a time-varying Hurst exponent. Inference is performed via integrated nested Laplace approximation, enabling joint estimation of mean trends and handling of irregularly sampled observations. The strengths and limitations of detecting changes in the autocorrelation is investigated in extensive simulations. Applied to real climatic data sets, we find evidence of early warning signals in a reconstructed Atlantic multidecadal variability index, while dismissing such signals for paleoclimate records spanning the Dansgaard-Oeschger events.

翻译：检测气候时间序列中的早期预警信号对于预测临界转变与临界点至关重要。常见的统计指标包括分岔点前增大的方差与滞后一阶自相关性。然而，这些指标对观测噪声、长期均值趋势以及长记忆依赖性均十分敏感，而这些特征在气候时间序列中普遍存在。此类效应极易掩盖真实信号或导致虚假检测。为应对这些挑战，我们采用一种灵活的贝叶斯框架，用于对长程依赖时间序列中随时间变化的自相关性进行建模，同时考虑时变方差。该方法通过混合两个分数高斯噪声过程，并使用时变权重函数来表示具有时变赫斯特指数的分数高斯噪声。推理通过集成嵌套拉普拉斯近似进行，从而能够联合估计均值趋势并处理不规则采样的观测数据。通过大量模拟研究，我们探讨了检测自相关性变化的优势与局限。将方法应用于实际气候数据集，我们在重建的大西洋多年代际变率指数中发现了早期预警信号的证据，而对于跨越丹斯加德-厄施格事件的古气候记录，则排除了此类信号的存在。