Sparse High-Frequency Volatility Estimation with Change-Point Detection

Summary

This paper develops sparse high-frequency volatility estimators designed to remain robust when spot volatility changes abruptly. The proposed estimators apply an ℓ1 penalty to existing methods, focusing on power variation estimators, a fundamental class for measuring volatility. The authors establish consistency for estimating both the underlying, unobserved volatility and the locations of its change points, with minimax rates achieved for particular estimators.

For computation, the method uses least angle regression to estimate candidate changes, followed by a reduced dynamic programming step to refine their number. Numerical results are described as fast and as accurately detecting breakpoints near the end of a sample. In out-of-sample forecasting, the estimators are reported to produce smoother and more realistic volatility forecasts and to outperform a broad range of classical and recent alternatives across different sampling frequencies and horizons. The supplied description does not give specific datasets, benchmarks, or numerical performance, limiting independent assessment of the comparison.

Key ideas

• The estimators use ℓ1 regularization to make high-frequency volatility estimates sparse and robust to abrupt changes.
• The paper studies power variation estimators and establishes consistency for volatility and change-point locations.
• Least angle regression finds candidate changes, and reduced dynamic programming refines their number.
• The authors report accurate late-sample breakpoint detection and improved out-of-sample forecasts across frequencies and horizons.

Tags

# High-Frequency Volatility Estimation with Fast Multiple Change Points Detection


# 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.

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