ON THE FUNCTIONAL ESTIMATION OF MULTIVARIATE DIFFUSION PROCESSES

Federico M. Bandi and Guillermo Moloche

Econometric Theory, 2018, vol. 34, issue 4, 896-946

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.

Date: 2018
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Working Paper: On the functional estimation of multivariate diffusion processes (2008)
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