Least squares estimators for discretely observed stochastic processes driven by small Lévy noises

Hongwei Long, Yasutaka Shimizu and Wei Sun

Journal of Multivariate Analysis, 2013, vol. 116, issue C, 422-439

Abstract: We study the problem of parameter estimation for discretely observed stochastic processes driven by additive small Lévy noises. We do not impose any moment condition on the driving Lévy process. Under certain regularity conditions on the drift function, we obtain consistency and rate of convergence of the least squares estimator (LSE) of the drift parameter when a small dispersion coefficient ε→0 and n→∞ simultaneously. The asymptotic distribution of the LSE in our general setting is shown to be the convolution of a normal distribution and a distribution related to the jump part of the Lévy process. Moreover, we briefly remark that our methodology can be easily extended to the more general case of semi-martingale noises.

Keywords: Asymptotic distribution of LSE; Consistency of LSE; Discrete observations; Least squares method; Stochastic processes; Parameter estimation; Small Lévy noises (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0047259X13000134
Full text for ScienceDirect subscribers only

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:eee:jmvana:v:116:y:2013:i:c:p:422-439

Ordering information: This journal article can be ordered from
http://www.elsevier.com/wps/find/supportfaq.cws_home/regional
https://shop.elsevie ... _01_ooc_1&version=01

DOI: 10.1016/j.jmva.2013.01.012

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 Catherine Liu ().