BaSTA: consistent multiscale multiple change-point detection for piecewise-stationary 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 a piecewise-stationary ARCH model for financial returns. 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 a particular choice of the transformation, and use simulation to fine-tune its parameter 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. Although the method is easy to implement, ready-made R software is provided.