漂移与突变：解耦趋势与变点分析
Drift vs Shift: Decoupling Trends and Changepoint Analysis
AI总结：
提出结合贝叶斯动态线性模型与惩罚似然估计的解耦方法，在复杂噪声下同时实现趋势平滑估计与变点精准检测，具有鲁棒性且可扩展至时变参数模型。
摘要：
我们引入了一种新方法，用于解耦时间序列中的趋势（漂移）和变点（突变）。我们基于局部自适应模型的方法用于稳健解耦，结合了贝叶斯趋势过滤和基于机器学习的正则化。首先应用过参数化的贝叶斯动态线性模型（DLM）来表征漂移。然后，将加权惩罚似然估计器与估计的DLM后验分布配对以识别突变。我们展示了使用所谓收缩先验指定的贝叶斯DLM如何在存在复杂噪声分量的情况下提供潜在趋势的平滑估计。然而，它们无法精确收缩至零的特性阻碍了直接的变点检测。相比之下，惩罚似然方法在定位变点方面非常有效。然而，它们要求信号和噪声模式均简单的数据。所提出的解耦方法结合了两者的优势，即贝叶斯DLM的灵活性与惩罚似然估计器的硬阈值特性，以在复杂的现代环境中提供变点分析。所提出的框架对异常值具有鲁棒性，能够识别多种变化，包括均值和斜率的变化。它也很容易扩展用于分析动态回归等时变参数模型中的参数突变。我们通过广泛的模拟和应用实例，展示了该方法的灵活性，并对比了其与几种替代方法的性能和鲁棒性。
英文摘要：
We introduce a new approach for decoupling trends (drift) and changepoints (shifts) in time series. Our locally adaptive model-based approach for robustly decoupling combines Bayesian trend filtering and machine learning based regularization. An over-parameterized Bayesian dynamic linear model (DLM) is first applied to characterize drift. Then a weighted penalized likelihood estimator is paired with the estimated DLM posterior distribution to identify shifts. We show how Bayesian DLMs specified with so-called shrinkage priors can provide smooth estimates of underlying trends in the presence of complex noise components. However, their inability to shrink exactly to zero inhibits direct changepoint detection. In contrast, penalized likelihood methods are highly effective in locating changepoints. However, they require data with simple patterns in both signal and noise. The proposed decoupling approach combines the strengths of both, i.e. the flexibility of Bayesian DLMs with the hard thresholding property of penalized likelihood estimators, to provide changepoint analysis in complex, modern settings. The proposed framework is outlier robust and can identify a variety of changes, including in mean and slope. It is also easily extended for analysis of parameter shifts in time-varying parameter models like dynamic regressions. We illustrate the flexibility and contrast the performance and robustness of our approach with several alternative methods across a wide range of simulations and application examples.
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