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

Author

Listed:
  • José E. Figueroa-López

    (Washington University)

  • Jeffrey Nisen

    (Quantitative Analytics, Barclays)

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.

Suggested Citation

  • José E. Figueroa-López & Jeffrey Nisen, 2019. "Second-order properties of thresholded realized power variations of FJA additive processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 431-474, October.
    • Handle: RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-019-09198-w
    DOI: 10.1007/s11203-019-09198-w
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    References listed on IDEAS

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    Cited by:

    1. José E. Figueroa-López & Cheng Li & Jeffrey Nisen, 2020. "Optimal iterative threshold-kernel estimation of jump diffusion processes," Statistical Inference for Stochastic Processes, Springer, vol. 23(3), pages 517-552, October.

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