Change point inference in high-dimensional regression models under temporal dependence

Haotian Xu, Daren Wang, Zifeng Zhao and Yi Yu
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Haotian Xu: Université catholique de Louvain, LIDAM/ISBA, Belgium

No 2022027, LIDAM Discussion Papers ISBA from Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA)

Abstract: This paper concerns about the limiting distributions of change point estimators, in a high- dimensional linear regression time series context, where a regression object (yt, Xt) ∈ R × Rp is observed at every time point t ∈ {1, . . . , n}. At unknown time points, called change points, the regression coefficients change, with the jump sizes measured in l2-norm. We provide limiting distributions of the change point estimators in the regimes where the minimal jump size vanishes and where it remains a constant. We allow for both the covariate and noise sequences to be temporally dependent, in the functional dependence framework, which is the first time seen in the change point inference literature. We show that a block-type long-run variance estimator is consistent under the functional dependence, which facilitates the practical implementation of our derived limiting distributions. We also present a few important byproducts of our analysis, which are of their own interest. These include a novel variant of the dynamic programming algorithm to boost the computational efficiency, consistent change point localisation rates under temporal dependence and a new Bernstein inequality for data possessing functional dependence. Extensive numerical results are provided to support our theoretical results. The proposed methods are implemented in the R package changepoints (Xu et al., 2021).

Keywords: High-dimensional linear regression; Change point inference; Functional dependence; Long-run variance; Confidence interval (search for similar items in EconPapers)
Pages: 107
Date: 2022-09-01
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