Estimation and Inference of Change Points in Functional Regression Time Series

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 investigation accommodates temporal dependence and heavy-tails in both the functional covariates and the measurement errors.Empirical performance of our method is demonstrated through extensive simulation studies and applications to financial Statistica Sinica: Newly accepted Paper and economic datasets.