Estimation for stochastic differential equations with a small diffusion coefficient

Arnaud Gloter and Michael Sørensen ()

Stochastic Processes and their Applications, 2009, vol. 119, issue 3, 679-699

Abstract: We consider a multidimensional diffusion X with drift coefficient b(Xt,[alpha]) and diffusion coefficient [epsilon]a(Xt,[beta]) where [alpha] and [beta] are two unknown parameters, while [epsilon] is known. For a high frequency sample of observations of the diffusion at the time points k/n, k=1,...,n, we propose a class of contrast functions and thus obtain estimators of ([alpha],[beta]). The estimators are shown to be consistent and asymptotically normal when n-->[infinity] and [epsilon]-->0 in such a way that [epsilon]-1n-[rho] remains bounded for some [rho]>0. The main focus is on the construction of explicit contrast functions, but it is noted that the theory covers quadratic martingale estimating functions as a special case. In a simulation study we consider the finite sample behaviour and the applicability to a financial model of an estimator obtained from a simple explicit contrast function.

Keywords: Asymptotics; CIR; model; Diffusion; process; with; small; noise; Discrete; time; observation; High; frequency; data; Minimum; contrast; estimation (search for similar items in EconPapers)
Date: 2009
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/S0304-4149(08)00071-9
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:spapps:v:119:y:2009:i:3:p:679-699

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

Access Statistics for this article

Stochastic Processes and their Applications is currently edited by T. Mikosch

More articles in Stochastic Processes and their Applications from Elsevier
Bibliographic data for series maintained by Catherine Liu ().