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Robust Estimation and Inference for Jumps in Noisy High Frequency Data: A Local‐to‐Continuity Theory for the Pre‐Averaging Method
Author(s) -
Li Jia
Publication year - 2013
Publication title -
econometrica
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 16.7
H-Index - 199
eISSN - 1468-0262
pISSN - 0012-9682
DOI - 10.3982/ecta10534
Subject(s) - estimator , mathematics , jump , asymptotic analysis , inference , limit (mathematics) , simple (philosophy) , econometrics , statistical physics , mathematical analysis , statistics , computer science , physics , quantum mechanics , artificial intelligence , philosophy , epistemology
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.