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 τ̂ 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 τ̂ 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.