Sparse inference of the drift of a high-dimensional Ornstein–Uhlenbeck process
Stéphane Gaïffas and
Journal of Multivariate Analysis, 2019, vol. 169, issue C, 1-20
Given the observation of a high-dimensional Ornstein–Uhlenbeck (OU) process in continuous time, we are interested in inference on the drift parameter under a row-sparsity assumption. Towards that aim, we consider the negative log-likelihood of the process, penalized by an ℓ1-penalization (Lasso and Adaptive Lasso). We provide both finite- and large-sample results for this procedure, by means of a sharp oracle inequality, and a limit theorem in the long-time asymptotics, including asymptotic consistency for variable selection. As a by-product, we point out the fact that for the Ornstein–Uhlenbeck process, one does not need an assumption of restricted eigenvalue type in order to derive fast rates for the Lasso, while it is well-known to be mandatory for linear regression for instance. Numerical results illustrate the benefits of this penalized procedure compared to standard maximum likelihood approaches both on simulations and real-world financial data.
Keywords: High-dimensional statistics; Lasso; Ornstein–Uhlenbeck process; Sparse estimation (search for similar items in EconPapers)
References: View references in EconPapers View complete reference list from CitEc
Citations Track citations by RSS feed
Downloads: (external link)
Full text for ScienceDirect subscribers only
This item may be available elsewhere in EconPapers: Search for items with the same title.
Export reference: BibTeX
RIS (EndNote, ProCite, RefMan)
Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:169:y:2019:i:c:p:1-20
Ordering information: This journal article can be ordered from
https://shop.elsevie ... _01_ooc_1&version=01
Access Statistics for this article
Journal of Multivariate Analysis is currently edited by de Leeuw, J.
More articles in Journal of Multivariate Analysis from Elsevier
Bibliographic data for series maintained by Dana Niculescu ().