使用动态模式分解检测时间序列中的状态转变
Detecting regime transitions in time series using dynamic mode decomposition
摘要：
我们采用的Koopman算子和动态模式分解的框架，设计一个计算成本低，易于实现的方法来检测瞬态动态和政权的变化时间序列。我们认为，典型的瞬态动力学经验的完整的状态空间维度，随后快速松弛的吸引子。另一方面，在平衡态中，动力学在较低维吸引子上以较慢的时间尺度演化。动态模式分解的重构误差被用来监测时间序列的无力，以解决对吸引子的快速松弛以及动态的有效维度。我们说明了我们的方法检测瞬态动力学的Kuramoto-Sivashinsky方程。我们进一步将我们的方法应用于大气再分析数据，我们的诊断检测从一个主要是负的北大西洋涛动（NAO）到一个主要是积极的NAO 1970年左右，以及最近发现的制度变化在南半球大气环流1970年左右的过渡。
英文摘要：
We employ the framework of the Koopman operator and dynamic mode decomposition to devise a computationally cheap and easily implementable method to detect transient dynamics and regime changes in time series. We argue that typically transient dynamics experiences the full state space dimension with subsequent fast relaxation towards the attractor. In equilibrium, on the other hand, the dynamics evolves on a slower time scale on a lower dimensional attractor. The reconstruction error of a dynamic mode decomposition is used to monitor the inability of the time series to resolve the fast relaxation towards the attractor as well as the effective dimension of the dynamics. We illustrate our method by detecting transient dynamics in the Kuramoto-Sivashinsky equation. We further apply our method to atmospheric reanalysis data; our diagnostics detects the transition from a predominantly negative North Atlantic Oscillation (NAO) to a predominantly positive NAO around 1970, as well as the recently found regime change in the Southern Hemisphere atmospheric circulation around 1970.
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