Nonparametric estimation of volatility models with serially dependent innovations

Christian Dahl and Michael Levine

Statistics & Probability Letters, 2006, vol. 76, issue 18, 2007-2016

Abstract: We are interested in modelling the time series process yt=[sigma](xt)[epsilon]t, where [epsilon]t=[phi]0[epsilon]t-1+vt. This model is of interest as it provides a plausible linkage between risk and expected return of financial assets. Further, the model can serve as a vehicle for testing the martingale difference sequence hypothesis, which is typically uncritically adopted in financial time series models. When xt has a fixed design, we provide a novel nonparametric estimator of the variance function based on the difference approach and establish its limiting properties. When xt is strictly stationary on a strongly mixing base (hereby allowing for ARCH effects) the nonparametric variance function estimator by Fan and Yao [1998. Efficient estimation of conditional variance functions in stochastic regression. Biometrika 85, 645-660] can be applied and seems very promising. We propose a semiparametric estimator of [phi]0 that is -consistent, adaptive, and asymptotic normally distributed under very general conditions on xt.

Keywords: Weak; form; volatility; models; Nonparametric/Semiparametric; estimation; Asymptotics (search for similar items in EconPapers)
Date: 2006
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (4)

Downloads: (external link)
http://www.sciencedirect.com/science/article/pii/S0167-7152(06)00187-8
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:stapro:v:76:y:2006:i:18:p:2007-2016

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

Access Statistics for this article

Statistics & Probability Letters is currently edited by Somnath Datta and Hira L. Koul

More articles in Statistics & Probability Letters from Elsevier
Bibliographic data for series maintained by Catherine Liu ().