Robust Jump Regressions

ABSTRACT We develop robust inference methods for studying linear dependence between the jumps of discretely observed processes at high frequency. Unlike classical linear regressions, jump regressions are determined by a small number of jumps occurring over a fixed time interval and the rest of the components of the processes around the jump times. The latter are the continuous martingale parts of the processes as well as observation noise. By sampling more frequently the role of these components, which are hidden in the observed price, shrinks asymptotically. The robustness of our inference procedure is with respect to outliers, which are of particular importance in the current setting of relatively small number of jump observations. This is achieved by using nonsmooth loss functions (like L1) in the estimation. Unlike classical robust methods, the limit of the objective function here remains nonsmooth. The proposed method is also robust to measurement error in the observed processes, which is achieved by locally smoothing the high-frequency increments. In an empirical application to financial data, we illustrate the usefulness of the robust techniques by contrasting the behavior of robust and ordinary least regression (OLS)-type jump regressions in periods including disruptions of the financial markets such as so-called “flash crashes.” Supplementary materials for this article are available online.

摘要我们开发了可靠的推理方法，以研究高频的离散观察过程的跳跃之间的线性依赖性。跳跃时间周围的过程是过程的连续部分以及观察噪声。隐藏在观察到的价格中，我们的推理程序的鲁棒性是相对于离群值的，这在当前相对较少的跳跃观测中尤为重要。 L1）在估计中，与经典的鲁棒方法不同，此处的目标函数的限制仍然不合时宜。观察到的过程是通过在经验应用中局部平滑高频增量来实现的。包括本文的“闪存崩溃”等金融市场的中断。