BaSTA: consistent multiscale multiple change-point detection for ARCH 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 ARCH model for financial returns with piecewise-constant parameter values. Our method, termed BaSTA (Binary Segmentation for Transformed ARCH), 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 FTSE 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. ∗Department of Statistics, Columbia House, London School of Economics, Houghton Street, London WC2A 2AE, UK. †Department of Statistics, Texas A&M University, 3143 TAMU, College Station, TX 77843-3143, USA.