Universität zu Köln

Lee, Wooyong, Greenwood, Priscilla E., Heckman, Nancy and Wefelmeyer, Wolfgang ORCID: 0000-0003-4814-0160 (2017). Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise. Stat. Infer. Stoch. Proc., 20 (2). S. 237 - 253. DORDRECHT: SPRINGER. ISSN 1572-9311

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Abstract

We consider estimation of the drift function of a stationary diffusion process when we observe high-frequency data with microstructure noise over a long time interval. We propose to estimate the drift function at a point by a Nadaraya-Watson estimator that uses observations that have been pre-averaged to reduce the noise. We give conditions under which our estimator is consistent and asympotically normal. Its rate and asymptotic bias and variance are the same as those without microstructure noise. To use our method in data analysis, we propose a data-based cross-validation method to determine the bandwidth in the Nadaraya-Watson estimator. Via simulation, we study several methods of bandwidth choices, and compare our estimator to several existing estimators. In terms of mean squared error, our new estimator outperforms existing estimators.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Lee, Wooyong UNSPECIFIED UNSPECIFIED UNSPECIFIED Greenwood, Priscilla E. UNSPECIFIED UNSPECIFIED UNSPECIFIED Heckman, Nancy UNSPECIFIED UNSPECIFIED UNSPECIFIED Wefelmeyer, Wolfgang UNSPECIFIED orcid.org/0000-0003-4814-0160 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-226887
DOI:	10.1007/s11203-016-9141-5
Journal or Publication Title:	Stat. Infer. Stoch. Proc.
Volume:	20
Number:	2
Page Range:	S. 237 - 253
Date:	2017
Publisher:	SPRINGER
Place of Publication:	DORDRECHT
ISSN:	1572-9311
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language Statistics & Probability Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/22688