Adaptive detection of multiple change-points in asset price volatility

This chapter considers the multiple change-point problem for time series, including strongly dependent processes, with an unknown number of change-points. We propose an adaptive method for finding the segmentation, i.e., the sequence of change-points τ with the optimal level of resolution. This optimal segmentation is obtained by minimizing a penalized contrast function J(τ, y)+βpen(τ). For a given contrast function J(τ, y) and a given penalty function pen(τ), the adaptive procedure for automatically choosing the penalization parameter β is such that the segmentation does not strongly depend on β. This algorithm is applied to the problem of detection of change-points in the volatility of financial time series, and compared with Vostrikova's (1981) binary segmentation procedure.