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On the functional estimation of multivariate diffusion processes

  • Bandi, Federico
  • Moloche, Guillermo

We propose a fully nonparametric estimation theory for 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. Minimal assumptions are imposed on the statistical properties of the multivariate system to obtain limiting results. Harris recurrence is all that we require to show strong consistency and asymptotic (mixed) normality of the functional estimates. Hence, the estimation method and asymptotic theory apply to both stationary and nonstationary multivariate diffusion processes of the recurrent type.

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File URL: http://mpra.ub.uni-muenchen.de/43681/1/MPRA_paper_43681.pdf
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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43681.

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Date of creation: 01 Jul 2008
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Handle: RePEc:pra:mprapa:43681
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  1. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, vol. 65(1), pages 81-101, December.
  2. repec:cup:cbooks:9780521355643 is not listed on IDEAS
  3. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
  4. repec:cup:cbooks:9780521586115 is not listed on IDEAS
  5. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  6. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
  7. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, vol. 71(1), pages 241-283, January.
  8. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
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