Robust Jump Regressions

Jia Li, Viktor Todorov, George Tauchen*

*Corresponding author for this work

Research output: Contribution to journalArticle

6 Scopus citations

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.

Original languageEnglish (US)
Pages (from-to)332-341
Number of pages10
JournalJournal of the American Statistical Association
Volume112
Issue number517
DOIs
StatePublished - Jan 2 2017

Keywords

  • High-frequency data
  • Jumps
  • Microstructure noise
  • Robust regression
  • Semimartingale

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

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