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On the functional estimation of multivariate diffusion processes

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  • Bandi, Federico
  • Moloche, Guillermo

Abstract

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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Bibliographic Info

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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Keywords: Diffusion processes; nonparametric estimation;

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References

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  1. Stanton, Richard, 1997. " A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, American Finance Association, vol. 52(5), pages 1973-2002, December.
  2. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, Cambridge University Press, number 9780521355643.
  3. Federico M. Bandi & Peter C. B. Phillips, 2003. "Fully Nonparametric Estimation of Scalar Diffusion Models," Econometrica, Econometric Society, Econometric Society, vol. 71(1), pages 241-283, January.
  4. Masry, Elias, 1996. "Multivariate regression estimation local polynomial fitting for time series," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 65(1), pages 81-101, December.
  5. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
  6. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 10(02), pages 316-356, June.
  7. 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, American Statistical Association, vol. 98, pages 118-134, January.
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Citations

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Cited by:
  1. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 26(02), pages 541-563, April.
  2. Aït-Sahalia, Yacine & Park, Joon Y., 2012. "Stationarity-based specification tests for diffusions when the process is nonstationary," Journal of Econometrics, Elsevier, Elsevier, vol. 169(2), pages 279-292.
  3. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
  4. Jiti Gao & Shin Kanaya & Degui Li & Dag Tjøstheim, 2013. "Uniform Consistency for Nonparametric Estimators in Null Recurrent Time Series," CREATES Research Papers 2013-29, School of Economics and Management, University of Aarhus.
  5. Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 321-357.
  6. Andrew Jeffrey, 2004. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(2), pages 251-289.
  7. Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, Elsevier, vol. 137(2), pages 354-395, April.
  8. Adam Canopius, 2006. "Practitioners' Corner," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 346-351.
  9. Annamaria Bianchi, 2009. "The normal approximation rate for the drift estimator of multidimensional diffusions," Statistical Inference for Stochastic Processes, Springer, Springer, vol. 12(3), pages 251-268, October.
  10. John Knight & Fuchun Li & Mingwei Yuan, 2006. "A Semiparametric Two-Factor Term Structure Model," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(2), pages 204-237.
  11. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, Cambridge University Press, vol. 24(05), pages 1174-1206, October.
  12. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
  13. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics, University of Gothenburg, Department of Economics 101, University of Gothenburg, Department of Economics.
  14. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, Princeton University Press, edition 1, volume 1, number 8355.

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