Multiple Change Point Detection in Reduced Rank High Dimensional Vector Autoregressive Models
Multiple Change Point Detection in Reduced Rank High Dimensional Vector Autoregressive Models
复制标题
降阶高维向量自回归模型的多变点检测
DOI：
10.1080/01621459.2022.2079514
复制
发表时间：
2021-09
影响因子：
3.7
通讯作者：
Peiliang Bai;Abolfazl Safikhani;G. Michailidis
中科院分区：
文献类型：
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作者：
Peiliang Bai;Abolfazl Safikhani;G. Michailidis
摘要研究了高维向量自回归（VAR）模型中转移矩阵具有低秩稀疏结构的变点检测与定位问题。我们首先解决的问题，检测一个单一的变化点，使用穷举搜索算法，并建立一个有限的样本误差界的准确性。接下来，我们将结果扩展到多个变化点的情况下，可以作为样本大小的函数增长。它们的检测基于两步算法，其中第一步，对重叠窗口采用候选变化点的穷举搜索，随后使用后向消除过程来筛选出冗余候选。两步策略产生一致的估计的数量和位置的变化点。为了减少计算成本，我们还研究了条件下，一个代理VAR模型与弱稀疏的过渡矩阵，可以准确地估计的变化点和它们的位置由原始模型产生的数据。这项工作还涉及并解决了正在考虑的VAR模型的性质所带来的一些新的技术挑战。所提出的算法和方法的有效性说明了合成和两个真实的数据集。本文的补充材料可在网上查阅。
ABSTRACT We study the problem of detecting and locating change points in high-dimensional Vector Autoregressive (VAR) models, whose transition matrices exhibit low rank plus sparse structure. We first address the problem of detecting a single change point using an exhaustive search algorithm and establish a finite sample error bound for its accuracy. Next, we extend the results to the case of multiple change points that can grow as a function of the sample size. Their detection is based on a two-step algorithm, wherein the first step, an exhaustive search for a candidate change point is employed for overlapping windows, and subsequently a backward elimination procedure is used to screen out redundant candidates. The two-step strategy yields consistent estimates of the number and the locations of the change points. To reduce computation cost, we also investigate conditions under which a surrogate VAR model with a weakly sparse transition matrix can accurately estimate the change points and their locations for data generated by the original model. This work also addresses and resolves a number of novel technical challenges posed by the nature of the VAR models under consideration. The effectiveness of the proposed algorithms and methodology is illustrated on both synthetic and two real datasets. Supplementary materials for this article are available online.