Econometrica: Jul 2013, Volume 81, Issue 4

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

https://doi.org/10.3982/ECTA10534
p. 1673-1693

Jia Li

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.

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

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

This supplement includes two appendices.  Supplemental Appendix A gives the proofs of the results in the main text.  Supplemental Appendix B provides simulation results of the theory in the main text.

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