Nonparametric Gaussian inference for stable processes

Fabian Mies () and Ansgar Steland ()
Additional contact information
Fabian Mies: RWTH Aachen University
Ansgar Steland: RWTH Aachen University

Statistical Inference for Stochastic Processes, 2019, vol. 22, issue 3, No 7, 525-555

Abstract: Abstract Jump processes driven by $$\alpha $$ α -stable Lévy processes impose inferential difficulties as their increments are heavy-tailed and the intensity of jumps is infinite. This paper considers the estimation of the functional drift and diffusion coefficients from high-frequency observations of a stochastic differential equation. By transforming the increments suitably prior to a regression, the variance of the emerging quantities may be bounded while allowing for identification of drift and diffusion in a single framework. These findings are applied to obtain a novel nonparametric kernel estimator, for which asymptotic normality and consistency of subsampling approximations are derived, and to a parametric volatility estimator for the Ornstein–Uhlenbeck process. The proposed approach also suggests a semiparametric estimator for the index of stability $$\alpha $$ α . Finite sample properties of the proposed estimators, in terms of mean (integrated) absolute error, are investigated by a simulation study and compared to their non-tempered counterparts.

Keywords: High-frequency data; Infinitesimal generator; Jumps; Kernel regression; Stable process; Subsampling (search for similar items in EconPapers)
Date: 2019
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1007/s11203-018-9193-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:sistpr:v:22:y:2019:i:3:d:10.1007_s11203-018-9193-9

Ordering information: This journal article can be ordered from
http://www.springer. ... ty/journal/11203/PS2

DOI: 10.1007/s11203-018-9193-9

Access Statistics for this article

Statistical Inference for Stochastic Processes is currently edited by Denis Bosq, Yury A. Kutoyants and Marc Hallin

More articles in Statistical Inference for Stochastic Processes from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().