Robust estimation and inference for jumps in noisy high frequency data: a local-tocontinuity theory for the pre-averaging method

We develop an asymptotic theory for the pre-averaging estimator when jumps are weakly identi\u85ed, here modeled as local to zero. The theory uni\u85es 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 identi\u85cation. We propose simple bias-corrected estimators for jump power variations, and construct robust con\u85dence sets with valid asymptotic size in a uniform sense. The method is also robust to microstructure noise. Monte Carlo evidence supports the theoretical \u85ndings. An empirical application to high frequency US stock returns data shows evidence for the weak identi\u85cation of jumps