Multiple-change-point detection for auto-regressive conditional heteroscedastic processes

• 成果类型: Article
• 署名作者: Fryzlewicz, P.; Rao, S. Subba
• 署名单位: University of London; London School Economics & Political Science; Texas A&M University System; Texas A&M University College Station
• 刊物名称: JOURNAL OF THE ROYAL STATISTICAL SOCIETY SERIES B-STATISTICAL METHODOLOGY
• ISSN/ISSBN: 1369-7412
• DOI: 10.1111/rssb.12054
• 发表日期: 2014
• 页码: 903-924
• 关键词: nonstationary time-series; least-squares estimation; varying arch processes; models

摘要

The emergence of the recent financial crisis, during which markets frequently underwent changes in their statistical structure over a short period of time, illustrates the importance of non-stationary modelling in financial time series. Motivated by this observation, we propose a fast, well performing and theoretically tractable method for detecting multiple change points in the structure of an auto-regressive conditional heteroscedastic model for financial returns with piecewise constant parameter values. Our method, termed BASTA (binary segmentation for transformed auto-regressive conditional heteroscedasticity), proceeds in two stages: process transformation and binary segmentation. The process transformation decorrelates the original process and lightens its tails; the binary segmentation consistently estimates the change points. We propose and justify two particular transformations and use simulation to fine-tune their parameters as well as the threshold parameter for the binary segmentation stage. A comparative simulation study illustrates good performance in comparison with the state of the art, and the analysis of the Financial Times Stock Exchange FTSE 100 index reveals an interesting correspondence between the estimated change points and major events of the recent financial crisis. Although the method is easy to implement, ready-made R software is provided.