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Detecting and dating structural breaks in functional data without dimension reduction
Author(s) -
Aue Alexander,
Rice Gregory,
Sönmez Ozan
Publication year - 2018
Publication title -
journal of the royal statistical society: series b (statistical methodology)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 6.523
H-Index - 137
eISSN - 1467-9868
pISSN - 1369-7412
DOI - 10.1111/rssb.12257
Subject(s) - estimator , functional principal component analysis , principal component analysis , dimension (graph theory) , dimensionality reduction , functional data analysis , relevance (law) , monte carlo method , feature (linguistics) , reduction (mathematics) , computer science , algorithm , mathematics , statistics , artificial intelligence , linguistics , philosophy , geometry , political science , pure mathematics , law
Summary 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.