Robust Jump Regressions

• 成果类型: Article
• 署名作者: Li, Jia; Todorov, Viktor; Tauchen, George
• 署名单位: Duke University; Northwestern University
• 刊物名称: JOURNAL OF THE AMERICAN STATISTICAL ASSOCIATION
• ISSN/ISSBN: 0162-1459
• DOI: 10.1080/01621459.2016.1138866
• 发表日期: 2017
• 页码: 332-341
• 关键词: realized kernels; noisy; variance; tale

摘要

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 L-1) 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.