Estimation and Inference for Change Points in Functional Regression Time Series

TL;DR

This paper introduces a new efficient method for detecting and estimating change points in functional linear regression models, with theoretical guarantees and practical validation on financial data.

Contribution

It proposes the FRBS algorithm for multiple change point detection in functional data, along with a refinement step and confidence interval construction under dependence and heavy tails.

Findings

FRBS achieves consistent change point detection.

Refinement improves localization accuracy.

Method performs well on simulated and real financial data.

Abstract

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.