Publication Type

Journal Article

Version

publishedVersion

Publication Date

5-2017

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.”

Keywords

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

Discipline

Econometrics | Economic Theory

Research Areas

Econometrics

Publication

Journal of the American Statistical Association

Volume

112

Issue

517

First Page

332

Last Page

341

ISSN

0162-1459

Identifier

10.1080/01621459.2016.1138866

Publisher

Taylor & Francis

Copyright Owner and License

Publisher

Additional URL

https://doi.org/10.1080/01621459.2016.1138866

Download

Share

COinS