Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local-to-Continuity Theory for the Pre-Averaging Method


  • Jia Li

    1. Dept. of Economics, Duke University, Durham, NC 27708, U.S.A.;
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    • 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.


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.