High-Frequency Volatility Estimation with Fast Multiple Change Points Detection

We propose a method for constructing sparse high-frequency volatility estimators that are robust against change points in the spot volatility process. The estimators we propose are $\ell_1$-regularized versions of existing volatility estimators. We focus on power variation estimators as they represent a fundamental class of volatility estimators. We establish consistency of these estimators for the true unobserved volatility and the change points locations, showing that minimax rates can be achieved for particular volatility estimators. The new estimators utilize the computationally efficient least angle regression algorithm for estimation purposes, followed by a reduced dynamic programming step to refine the final number of change points. In terms of numerical performance, these estimators are not only computationally fast but also accurately identify breakpoints near the end of the sample, both features highly desirable in today's electronic trading environment. In terms of out-of-sample volatility prediction, our new estimators provide more realistic and smoother volatility forecasts, outperforming a broad range of classical and recent volatility estimators across various frequencies and forecasting horizons.