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Bandwidth selection for continuous-time Markov processes

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Author Info

  • Bandi, Federico
  • Corradi, Valentina
  • Moloche, Guillermo

Abstract

We propose a theoretical approach to bandwidth choice for continuous-time Markov processes. We do so in the context of stationary and nonstationary processes of the recurrent kind. The procedure consists of two steps. In the first step, by invoking local Gaussianity, we suggest an automated bandwidth selection method which maximizes the probability that the standardized data are a collection of normal draws. In the case of diffusions, for instance, this procedure selects a bandwidth which only ensures consistency of the infinitesimal variance estimator, not of the drift estimator. Additionally, the procedure does not guarantee that the rate conditions for asymptotic normality of the infinitesimal variance estimator are satisfied. In the second step, we propose tests of the hypothesis that the bandwidth(s) are either "too small" or "too big" to satisfy all necessary rate conditions for consistency and asymptotic normality. The suggested statistics rely on a randomized procedure based on the idea of conditional inference. Importantly, if the null is rejected, then the first-stage bandwidths are kept. Otherwise, the outcomes of the tests indicate whether larger or smaller bandwidths should be selected. We study scalar and multivariate diffusion processes, jump-diffusion processes, as well as processes measured with error as is the case, for instance, for stochastic volatility modelling by virtue of preliminary high-frequency spot variance estimates. The finite sample joint behavior of our proposed automated bandwidth selection method, as well as that of the associated (second-step) randomized procedure, are studied via Monte Carlo simulation.

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Bibliographic Info

Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 43682.

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Date of creation: 30 Oct 2009
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Handle: RePEc:pra:mprapa:43682

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Related research

Keywords: Diffusion processes; nonparametric estimation;

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References

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  1. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
  2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-27, July.
  3. Bandi, Federico M. & Phillips, Peter C.B., 2007. "A simple approach to the parametric estimation of potentially nonstationary diffusions," Journal of Econometrics, Elsevier, vol. 137(2), pages 354-395, April.
  4. Valentina Corradi & Norman R. Swanson, 2003. "The Effect of Data Transformation on Common Cycle, Cointegration and Unit Root Tests: Monte Carlo Results and a Simple Test," Departmental Working Papers 200322, Rutgers University, Department of Economics.
  5. 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.
  6. Bandi, Federico M. & Nguyen, Thong H., 2003. "On the functional estimation of jump-diffusion models," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 293-328.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March.
  8. Federico M. Bandi & Peter C.B. Phillips, 2001. "Fully Nonparametric Estimation of Scalar Diffusion Models," Cowles Foundation Discussion Papers 1332, Cowles Foundation for Research in Economics, Yale University.
  9. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
  10. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  11. Bandi, Federico & Moloche, Guillermo, 2008. "On the functional estimation of multivariate diffusion processes," MPRA Paper 43681, University Library of Munich, Germany.
  12. Dennis Kristensen, 2007. "Nonparametric Filtering of the Realised Spot Volatility: A Kernel-based Approach," CREATES Research Papers 2007-02, School of Economics and Management, University of Aarhus.
  13. 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.
  14. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 2002. "Bayesian Analysis of Stochastic Volatility Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 69-87, January.
  15. Shin Kanaya & Dennis Kristensen, 2010. "Estimation of Stochastic Volatility Models by Nonparametric Filtering," CREATES Research Papers 2010-67, School of Economics and Management, University of Aarhus.
  16. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, 02.
  17. Jacquier, Eric & Polson, Nicholas G & Rossi, Peter E, 1994. "Bayesian Analysis of Stochastic Volatility Models: Comments: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 413-17, October.
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Cited by:
  1. Norman R. Swanson & Valentina Corradi & Walter Distaso, 2011. "Predictive Inference for Integrated Volatility," Departmental Working Papers 201108, Rutgers University, Department of Economics.
  2. Nikolay Gospodinov & Masayuki Hirukawa, 2008. "Nonparametric Estimation of Scalar Diffusion Processes of Interest Rates Using Asymmetric Kernels," Working Papers 08011, Concordia University, Department of Economics, revised Dec 2008.

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