Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading

Ole E. Barndorff-Nielsen (1) , Peter Reinhard Hansen (2) , Asger Lunde (3) , Neil Shephard (4, 5)

1 Department of Mathematical Sciences
2 Department of Economics
3 Aarhus University [Aarhus]
4 University of Oxford
5 Department of Economics

We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to measurement error of certain types and can also handle non-synchronous trading. It is the first estimator which has these three properties which are all essential for empirical work in this area. We derive the large sample asymptotics of this estimator and assess its accuracy using a Monte Carlo study. We implement the estimator on some US equity data, comparing our results to previous work which has used returns measured over 5 or 10 min intervals. We show that the new estimator is substantially more precise.

Mots clés: HAC estimator; Long run variance estimator; Market frictions; Quadratic variation; Realised variance

Domaines: Econométrie de la finance [q-fin.ST]

Ole E. Barndorff-Nielsen, Peter Reinhard Hansen, Asger Lunde, Neil Shephard. Multivariate realised kernels: Consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading. Econometrics, 2011, 162 (2), pp.149. ⟨10.1016/j.jeconom.2010.07.009⟩. ⟨hal-00815564⟩