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

José E. Figueroa-López; Jeffrey Nisen

doi:10.1007/s11203-019-09198-w

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

José E. Figueroa-López
, Jeffrey Nisen

Research output: Contribution to journal › Article › peer-review

1 Scopus citations

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.

Original language	English
Pages (from-to)	431-474
Number of pages	44
Journal	Statistical Inference for Stochastic Processes
Volume	22
Issue number	3
DOIs	https://doi.org/10.1007/s11203-019-09198-w
State	Published - Oct 15 2019

Keywords

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

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10.1007/s11203-019-09198-w

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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 L{\'e}vy 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.",

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AU - Figueroa-López, José E.

AU - Nisen, Jeffrey

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N2 - 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.

AB - 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.

KW - Additive processes

KW - Integrated variance estimation

KW - Jump features estimation

KW - Lévy processes

KW - Multipower realized variations

KW - Nonparametric estimation

KW - Truncated realized variations

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EP - 474

JO - Statistical Inference for Stochastic Processes

JF - Statistical Inference for Stochastic Processes

IS - 3

ER -

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

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