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ON THE FUNCTIONAL ESTIMATION OF MULTIVARIATE DIFFUSION PROCESSES

Published online by Cambridge University Press:  18 September 2017

Federico M. Bandi  and
Guillermo Moloche
Federico M. Bandi*
Affiliation:
Johns Hopkins University and Edhec-Risk Institute
Guillermo Moloche
Affiliation:
fermat.ai
*
*Address correspondence to Federico Bandi, Johns Hopkins Carey Business School, 100 International Drive, Baltimore, MD 21202, USA; e-mail: fbandi1@jhu.edu.
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Abstract

We propose a nonparametric estimation theory for the occupation density, the drift vector, and the diffusion matrix of multivariate diffusion processes. The estimators are sample analogues to infinitesimal conditional expectations constructed as Nadaraya-Watson kernel averages. Mild assumptions are imposed on the statistical properties of the multivariate system to obtain limiting results. Harris recurrence is all that we require to show consistency and asymptotic (mixed) normality of the proposed functional estimators. The identification method and asymptotic theory apply to both stationary and nonstationary multivariate diffusion processes of the recurrent type.

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ARTICLES
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Econometric Theory , Volume 34 , Issue 4 , August 2018 , pp. 896 - 946
Copyright
Copyright © Cambridge University Press 2017 

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Footnotes

We are especially grateful to Valentina Corradi for helpful discussions. We thank Xiaohong Chen, the Editor Peter C.B. Phillips, and four anonymous referees for their very useful comments. Seminar participants at various institutions and conferences have also provided suggestions for which we are thankful. Bandi acknowledges financial support from the IBM Corporation Faculty Research Fund at Chicago Booth, University of Chicago, and from Carey Business School, Johns Hopkins University.

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