Abstract

Assuming stationarity is unrealistic in many time series applications. A more realistic alternative is to assume piecewise stationarity, where the model can change at potentially many change points. We propose a three-stage procedure for simultaneous estimation of change points and parameters of high-dimensional piecewise vector autoregressive (VAR) models. In the first step, we reformulate the change point detection problem as a high-dimensional variable selection one, and solve it using a penalized least square estimator with a total variation penalty. We show that the penalized estimation method over-estimates the number of change points, and propose a selection criterion to identify the change points. In the last step of our procedure, we estimate the VAR parameters in each of the segments. We prove that the proposed procedure consistently detects the number and location of change points, and provides consistent estimates of VAR parameters. The performance of the method is illustrated through several simulated and real data examples. Supplementary materials for this article are available online.

 抽象的

在许多时间序列应用中假设平稳性是不现实的。更现实的替代方案是假设分段平稳性，其中模型可能在许多潜在的变化点处发生变化。我们提出了一种三阶段程序，用于同时估计高维分段向量自回归（VAR）模型的变化点和参数。第一步，我们将变化点检测问题重新表述为高维变量选择问题，并使用带有总变差惩罚的惩罚最小二乘估计器来解决它。我们证明了惩罚估计方法高估了变化点的数量，并提出了识别变化点的选择标准。在我们程序的最后一步中，我们估计每个分段中的 VAR 参数。我们证明所提出的程序能够一致地检测变化点的数量和位置，并提供一致的 VAR 参数估计。通过几个模拟和实际数据示例说明了该方法的性能。本文的补充材料可在线获取。