Detecting and dating structural breaks in functional data without dimension reduction

• 成果类型: Article
• 署名作者: Aue, Alexander; Rice, Gregory; Sonmez, Ozan
• 署名单位: University of California System; University of California Davis; University of Waterloo
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12257
• 发表日期: 2018
• 页码: 509-529
• 关键词: time-series; random-fields; stationarity; projections

摘要

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.