Estimation and Inference for Change Points in Functional Regression Time Series
arxiv(2024)
摘要
In this paper, we study the estimation and inference of change points under a
functional linear regression model with changes in the slope function. We
present a novel Functional Regression Binary Segmentation (FRBS) algorithm
which is computationally efficient as well as achieving consistency in multiple
change point detection. This algorithm utilizes the predictive power of
piece-wise constant functional linear regression models in the reproducing
kernel Hilbert space framework. We further propose a refinement step that
improves the localization rate of the initial estimator output by FRBS, and
derive asymptotic distributions of the refined estimators for two different
regimes determined by the magnitude of a change. To facilitate the construction
of confidence intervals for underlying change points based on the limiting
distribution, we propose a consistent block-type long-run variance estimator.
Our theoretical justifications for the proposed approach accommodate temporal
dependence and heavy-tailedness in both the functional covariates and the
measurement errors. Empirical effectiveness of our methodology is demonstrated
through extensive simulation studies and an application to the Standard and
Poor's 500 index dataset.
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