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

José E. Figueroa-López () and Jeffrey Nisen ()
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José E. Figueroa-López: Washington University
Jeffrey Nisen: Quantitative Analytics, Barclays

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 4, 474 pages

Abstract: 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 (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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DOI: 10.1007/s11203-019-09198-w

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