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

References in zbMATH (referenced in 13 articles , 1 standard article )

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  1. Diop, Mamadou Lamine; Kengne, William: Piecewise autoregression for general integer-valued time series (2021)
  2. Pang, Tianxiao; Du, Lingjie; Chong, Terence Tai-Leung: Estimating multiple breaks in nonstationary autoregressive models (2021)
  3. Cai, Li; Li, Lisha; Huang, Simin; Ma, Liang; Yang, Lijian: Oracally efficient estimation for dense functional data with holiday effects (2020)
  4. Dufays, Arnaud; Rombouts, Jeroen V. K.: Relevant parameter changes in structural break models (2020)
  5. Li, Yingbo; Lund, Robert; Hewaarachchi, Anuradha: Multiple changepoint detection with partial information on changepoint times (2019)
  6. Barigozzi, Matteo; Cho, Haeran; Fryzlewicz, Piotr: Simultaneous multiple change-point and factor analysis for high-dimensional time series (2018)
  7. Fryzlewicz, Piotr: Tail-greedy bottom-up data decompositions and fast multiple change-point detection (2018)
  8. Galeano, Pedro; Wied, Dominik: Dating multiple change points in the correlation matrix (2017)
  9. Bardet, Jean-Marc; Kengne, William: Monitoring procedure for parameter change in causal time series (2014)
  10. Fryzlewicz, Piotr: Wild binary segmentation for multiple change-point detection (2014)
  11. Fryzlewicz, P.; Rao, S. Subba: Multiple-change-point detection for auto-regressive conditional heteroscedastic processes (2014)
  12. Hušková, Marie; Prášková, Zuzana: Comments on: “Extensions of some classical methods in change point analysis” (2014)
  13. Fryzlewicz, Piotr; Schröder, Anna Louise: Adaptive trend estimation in financial time series via multiscale change-point-induced basis recovery (2013)