High-Frequency Volatility Estimation with Fast Multiple Change Points Detection

We propose high-frequency volatility estimators with multiple change points that are $\ell_1$-regularized versions of two classical estimators: quadratic variation and bipower variation. We establish consistency of these estimators for the true unobserved volatility and the change points locations under general sub-Weibull distribution assumptions on the jump process. The proposed estimators employ 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, the proposed estimators are computationally fast and accurately identify breakpoints near the end of the sample, which is 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, and they outperform a wide range of classical and recent volatility estimators across various frequencies and forecasting horizons.