Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise |
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Authors: | Wooyong Lee Priscilla E Greenwood Nancy Heckman Wolfgang Wefelmeyer |
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Institution: | 1.Department of Economics,University of Chicago,Chicago,USA;2.Statistics Department,University of British Columbia,Vancouver,Canada;3.Mathematical Institute,University of Cologne,Cologne,Germany |
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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. |
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