Econometrics of co-jumps in high-frequency data with noise

Abstract

We establish estimation methods to determine co-jumps in multivariate high-frequency data with nonsynchronous observations and market microstructure noise. The ex-post quadratic covariation of the signal part, which is modeled by an Itô-semimartingale, is estimated with a locally adaptive spectral approach. Locally adaptive thresholding allows to disentangle the co-jump and continuous part in quadratic covariation. Our estimation procedure implicitly renders spot (co-)variance estimators. We derive a feasible stable limit theorem for a truncated spectral estimator of integrated covariance. A test for common jumps is obtained with a wild bootstrap strategy. We give an explicit guideline how to implement the method and test the algorithm in Monte Carlo simulations. An empirical application to intra-day tick-data demonstrates the practical value of the approach.

Estimation of the discontinuous leverage effect: Evidence from the NASDAQ order book

“…Section 3.3 discusses our solution. Related problems by not knowing the exact timing of jumps arise and have been addressed in different ways in Vetter (2014) and Bibinger and Winkelmann (2015). …”

“…To estimate changes in the quadratic variation, ∆ k [X, X], on bins with a price jump, we adapt the statistics from Section 3.1.3 of Bibinger and Winkelmann (2015) and define…”

“…To detect price-jump times, we refine the adaptive thresholding approach of Bibinger and Winkelmann (2015). We construct an argmax-estimator, such as is often used in changepoint analysis.…”

“…Estimating the entire quadratic variation with jumps or testing for jumps over a whole day are related yet different problems. Jacod et al (2010) and Koike (2017) have developed rate-optimal consistent pre-average estimators for the quadratic variation and Bibinger and Winkelmann (2015) provide spectral estimators for this purpose. While these methods do not recover individual price jumps, the Lee and Mykland (2012) method utilizes natural local average statistics to address inference on price jumps under noise.…”

Do Co-Jumps Impact Correlations in Currency Markets?

“…In addition, Mancini and Gobbi (2012) observe co-jumps via thresholding techniques. Recently, spectral techniques for co-jump detection have been employed by Bibinger and Winkelmann (2015). Gilder et al (2014) use the approach of Bollerslev et al (2008) to identify co-jumps at daily frequency.…”