Journal Article

Detecting and dating structural breaks in functional data without dimension reduction

Aue, Alexander, Sönmez, Ozan, Rice, Gregory

2018

Overview

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 estimators based on functional principal component analysis 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 procedures proposed.

• Publisher: Wiley,Oxford University Press
• Subject: Asymptotic methods / Change point analysis / Computer simulation / confidence interval / Confidence intervals / Data / Dating techniques / Economic models / equations / Functional data / Functional principal components / Functional time series / mathematical theory / Monte Carlo method / Monte Carlo simulation / principal component analysis / Principal components analysis / Reduction / Regression analysis / Simulation / Statistical methods / Statistics / Structural breaks / temperature / Temperature data