Detecting and dating structural breaks in functional data without dimension reduction

TL;DR

This paper introduces a fully functional method for detecting and dating structural breaks in functional data without relying on dimension reduction, providing robust theoretical and practical tools.

Contribution

It develops a new fully functional break detection procedure with asymptotic theory and confidence intervals, outperforming PCA-based methods in certain scenarios.

Findings

Fully functional procedures outperform PCA-based methods when features are orthogonal to principal components.

Theoretical results are validated through Monte Carlo simulations.

Application to temperature data demonstrates practical utility.

Abstract

Methodology is proposed to uncover structural breaks in functional data that is "fully functional" in the sense that it does not rely on dimension reduction techniques. A thorough asymptotic theory is developed for a fully functional break detection procedure as well as for a break date estimator, assuming a fixed break size and a shrinking break size. The latter result is utilized to derive confidence intervals for the unknown break date. The main results highlight that the fully functional procedures perform best under conditions when analogous fPCA based estimators are at their worst, namely when the feature of interest is orthogonal to the leading principal components of the data. The theoretical findings are confirmed by means of a Monte Carlo simulation study in finite samples. An application to annual temperature curves illustrates the practical relevance of the proposed procedures.