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Detecting dynamical changes in nonlinear time series using locally linear state‐space models

机译：使用局部线性状态空间模型检测非线性时间序列中的动态变化

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Interest is growing in methods for predicting and detecting regime shifts—changes in the structure of dynamical processes that cause shifts among alternative stable states. Here, we use locally linear, autoregressive state‐space models to statistically identify nonlinear processes that govern the dynamics of time series. We develop both time‐varying and threshold models. In time‐varying autoregressive models with p time lags, AR(p ), and vector autoregressive models for n ‐dimensional systems of order p = 1, VAR(1), we assume that coefficients vary with time. We can infer an approaching regime shift if the coefficients indicate critical slowing down of the local dynamics of the system. In self‐excited threshold models, we assume that the time series is governed by two autoregressive processes; the state variable switches between them when the time series crosses a threshold value. We use the existence of a statistically significant threshold as an indicator of alternative stable states. All models are fit to data using a state‐space form that incorporates measurement error, and maximum likelihood estimation allows for statistically testing alternative hypotheses about the processes governing dynamics. Our model‐based approach for forecasting regime shifts and identifying alternative stable states overcomes limitations of other common metric‐based approaches and is a useful addition to the toolbox of methods for analyzing nonlinear time series.
机译：预测和检测状态变化的方法越来越引起人们的兴趣，这种方法是动态过程结构的变化，这种变化会导致可替代的稳定状态之间发生变化。在这里，我们使用局部线性，自回归状态空间模型来统计地识别控制时间序列动态的非线性过程。我们同时开发时变模型和阈值模型。在具有 p个时间滞后，AR（ p）的时变自回归模型和 p阶1 = VAR（1）的 n个维系统的向量自回归模型中，我们假设系数随时间变化。如果系数表明系统局部动力学的严重减慢，我们可以推断出即将到来的体制转变。在自激阈值模型中，我们假设时间序列受两个自回归过程控制;当时间序列超过阈值时，状态变量将在它们之间切换。我们使用存在统计学意义的阈值作为替代稳定状态的指标。所有模型都使用包含测量误差的状态空间形式来拟合数据，并且最大似然估计允许统计测试关于控制动态过程的替代假设。我们用于预测状态变化和识别替代稳态的基于模型的方法克服了其他常见的基于度量的方法的局限性，是对分析非线性时间序列的方法工具箱的有益补充。

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