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Second-order properties of thresholded realized power variations of FJA additive processes

  • José E. Figueroa-LópezEmail author
  • Jeffrey Nisen
Article
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Abstract

For a class of additive processes of finite jump activity (FJA), we give precise conditions for the mean-squared consistency and feasible Central Limit Theorems of thresholded realized power variation estimators (TRV). To justify that the proposed conditions are the “best possible”, we also show that these are necessary for FJA Lévy processes. Non-asymptotic upper bounds and asymptotic decompositions of the mean-squared errors of our estimators are also provided. For comparison purposes, we also obtain the analogous asymptotic decomposition for a general multi-power realized variation (MPV). These results theoretically justify the relatively large bias of MPV (when compared to TRV) observed numerically in earlier Monte Carlo studies.

Keywords

Truncated realized variations Multipower realized variations Integrated variance estimation Jump features estimation Lévy processes Additive processes Nonparametric estimation 

Notes

Acknowledgements

The first author’s research was partially supported by the NSF Grants DMS-1561141 and DMS-1613016. Both authors are thankful to two anonymous referees for many insightful and helpful comments.

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Copyright information

© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsWashington UniversitySt. LouisUSA
  2. 2.Quantitative Analytics, BarclaysNew YorkUSA

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