This paper is a revised version of part of my Ph.D. dissertation at the Department of Economics, Princeton University. I am very grateful to my advisors Yacine Aït-Sahalia, Ulrich Müller, and Mark Watson, as well as Jean Jacod, for their guidance. I am also grateful for comments from Tim Bollerslev, Valentina Corradi, Nour Meddahi, Andrew Patton, George Tauchen, and Viktor Todorov on various versions of this paper. Comments from three referees, a co-editor, and a guest co-editor have vastly improved the paper. This work is partially supported by NSF Grant SES-1227448. All errors are mine.
Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method
Article first published online: 26 JUL 2013
© 2013 The Econometric Society
Volume 81, Issue 4, pages 1673–1693, July 2013
How to Cite
Li, J. (2013), Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method. Econometrica, 81: 1673–1693. doi: 10.3982/ECTA10534
- Issue published online: 26 JUL 2013
- Article first published online: 26 JUL 2013
- Manuscript received January, 2012; final revision received January, 2013.
- Confidence set;
- high frequency data;
- jump power variation;
- market microstructure noise;
We develop an asymptotic theory for the pre-averaging estimator when asset price jumps are weakly identified, here modeled as local to zero. The theory unifies the conventional asymptotic theory for continuous and discontinuous semimartingales as two polar cases with a continuum of local asymptotics, and explains the breakdown of the conventional procedures under weak identification. We propose simple bias-corrected estimators for jump power variations, and construct robust confidence sets with valid asymptotic size in a uniform sense. The method is also robust to certain forms of microstructure noise.