We would like to thank a co-editor and two anonymous referees for their detailed and thoughtful comments, which helped greatly improve the paper. We would also like to thank Yacine Aït-Sahalia, Torben G. Andersen, Richard Davis, Jean Jacod, Thomas Mikosch, Mark Podolskij, Eric Renault, George Tauchen, as well as seminar participants at various conferences for many useful suggestions. The research was partly funded by NSF grant SES-0957330 to the NBER. Bollerslev also acknowledges support from CREATES funded by the Danish National Research Foundation.
Estimation of Jump Tails
Article first published online: 22 NOV 2011
© 2011 The Econometric Society
Volume 79, Issue 6, pages 1727–1783, November 2011
How to Cite
Bollerslev, T. and Todorov, V. (2011), Estimation of Jump Tails. Econometrica, 79: 1727–1783. doi: 10.3982/ECTA9240
- Issue published online: 22 NOV 2011
- Article first published online: 22 NOV 2011
- Manuscript received April, 2010; final revision received June, 2011.
- Extreme events;
- high-frequency data;
- jump tails;
- nonparametric estimation;
- stochastic volatility
We propose a new and flexible nonparametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple-to-implement set of estimating equations associated with the compensator for the jump measure, or its intensity, that only utilizes the weak assumption of regular variation in the jump tails, along with in-fill asymptotic arguments for directly estimating the “large” jumps. The procedure assumes that the large-sized jumps are identically distributed, but otherwise allows for very general dynamic dependencies in jump occurrences, and, importantly, does not restrict the behavior of the “small” jumps or the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high-frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature.