A1748
Title: Estimation and inference for change points in functional regression time series
Authors: Shivam Kumar - University of Chicago (United States) [presenting]
Haotian Xu - Auburn University (United States)
Daren Wang - University of Notre Dame (United States)
Abstract: Change point estimation and inference under a Functional linear Regression model with changes in the slope function is studied. A novel Functional Regression Binary Segmentation (FRBS) algorithm is presented, which is computationally efficient and achieves consistency in multiple change point detection. The algorithm utilizes the predictive power of piecewise constant Functional linear Regression models in the reproducing kernel Hilbert space framework. A refinement step is proposed that improves the localization rate of the initial estimator output by FRBS, and asymptotic distributions of the refined estimators are derived 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, a consistent block-type long-run variance estimator is proposed. Theoretical justifications for the proposed approach accommodate temporal dependence and heavy-tailedness in both the Functional covariates and the measurement errors. Empirical effectiveness of the methodology is demonstrated through extensive simulation studies and an application to the Standard and Poors 500 index dataset.
