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Preprint
Efficient Integrated Volatility Estimation in the Presence of Infinite Variation Jumps via Debiased Truncated Realized Variations
arXiv (Cornell University)
21 Sep 2022
Abstract
Statistical inference for stochastic processes based on high-frequency
observations has been an active research area for more than two decades. One of
the most well-known and widely studied problems is the estimation of the
quadratic variation of the continuous component of an It\^o semimartingale with
jumps. Several rate- and variance-efficient estimators have been proposed in
the literature when the jump component is of bounded variation. However, to
date, very few methods can deal with jumps of unbounded variation. By
developing new high-order expansions of the truncated moments of a locally
stable L\'evy process, we construct a new rate- and variance-efficient
volatility estimator for a class of It\^o semimartingales whose jumps behave
locally like those of a stable L\'evy process with Blumenthal-Getoor index
$Y\in (1,8/5)$ (hence, of unbounded variation). The proposed method is based on
a two-step debiasing procedure for the truncated realized quadratic variation
of the process. Our Monte Carlo experiments indicate that the method
outperforms other efficient alternatives in the literature in the setting
covered by our theoretical framework.
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Details
- Title
- Efficient Integrated Volatility Estimation in the Presence of Infinite Variation Jumps via Debiased Truncated Realized Variations
- Creators
- B. Cooper BonieceJosé E Figueroa-LópezYuchen Han
- Publication Details
- arXiv (Cornell University)
- Resource Type
- Preprint
- Language
- English
- Academic Unit
- Mathematics
- Other Identifier
- 991021861621004721