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Estimation of Jump Tails

  • Tim Bollerslev
  • Viktor Todorov

We propose a new and flexible non-parametric 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 uniquely identifying the \large" jumps from the data. The estimation allows for very general dynamic dependencies in the jump tails, and does not restrict 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.

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Article provided by Econometric Society in its journal Econometrica.

Volume (Year): 79 (2011)
Issue (Month): 6 (November)
Pages: 1727-1783

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Handle: RePEc:ecm:emetrp:v:79:y:2011:i:6:p:1727-1783
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  1. George Tauchen & Viktor Todorov, 2010. "Activity Signature Functions for High-Frequency Data Analysis," Working Papers 10-08, Duke University, Department of Economics.
  2. Neil Shephard & Ole Barndorff-Nielsen, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Series Working Papers 2004-FE-01, University of Oxford, Department of Economics.
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  10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling and Forecasting of Return Volatility," CREATES Research Papers 2007-18, School of Economics and Management, University of Aarhus.
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