IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v34y2018i04p896-946_00.html
   My bibliography  Save this article

On The Functional Estimation Of Multivariate Diffusion Processes

Author

Listed:
  • Bandi, Federico M.
  • Moloche, Guillermo

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.

Suggested Citation

  • Bandi, Federico M. & Moloche, Guillermo, 2018. "On The Functional Estimation Of Multivariate Diffusion Processes," Econometric Theory, Cambridge University Press, vol. 34(4), pages 896-946, August.
    • Handle: RePEc:cup:etheor:v:34:y:2018:i:04:p:896-946_00
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466617000305/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Wang, Qiying & Phillips, Peter C.B., 2009. "Asymptotic Theory For Local Time Density Estimation And Nonparametric Cointegrating Regression," Econometric Theory, Cambridge University Press, vol. 25(3), pages 710-738, June.
    3. 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.
    4. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    5. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(2), pages 316-356, June.
    6. 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.
    7. 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.
    8. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
    9. 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.
    10. Haya Kaspi & Avi Mandelbaum, 1994. "On Harris Recurrence in Continuous Time," Mathematics of Operations Research, INFORMS, vol. 19(1), pages 211-222, February.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Hjalmarsson, Erik, 2003. "Does the Black-Scholes formula work for electricity markets? A nonparametric approach," Working Papers in Economics 101, University of Gothenburg, Department of Economics.
    2. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    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. Adam Canopius, 2006. "Practitioners' Corner," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 346-351.
    5. Gao, Jiti & Kanaya, Shin & Li, Degui & Tjøstheim, Dag, 2015. "Uniform Consistency For Nonparametric Estimators In Null Recurrent Time Series," Econometric Theory, Cambridge University Press, vol. 31(5), pages 911-952, October.
    6. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    7. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
    8. Bu, Ruijun & Kim, Jihyun & Wang, Bin, 2023. "Uniform and Lp convergences for nonparametric continuous time regressions with semiparametric applications," Journal of Econometrics, Elsevier, vol. 235(2), pages 1934-1954.
    9. Aït-Sahalia, Yacine & Park, Joon Y., 2012. "Stationarity-based specification tests for diffusions when the process is nonstationary," Journal of Econometrics, Elsevier, vol. 169(2), pages 279-292.
    10. Andrew Jeffrey, 2004. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Journal of Financial Econometrics, Oxford University Press, vol. 2(2), pages 251-289.
    11. Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 321-357.
    12. Annamaria Bianchi, 2009. "The normal approximation rate for the drift estimator of multidimensional diffusions," Statistical Inference for Stochastic Processes, Springer, vol. 12(3), pages 251-268, October.
    13. John Knight & Fuchun Li & Mingwei Yuan, 2006. "A Semiparametric Two-Factor Term Structure Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 204-237.
    14. Fabian Mies & Ansgar Steland, 2019. "Nonparametric Gaussian inference for stable processes," Statistical Inference for Stochastic Processes, Springer, vol. 22(3), pages 525-555, October.
    15. Yuping Song & Weijie Hou & Guang Yang, 2020. "Asymptotic Normality of Convoluted Smoothed Kernel Estimation for Scalar Diffusion Model," Methodology and Computing in Applied Probability, Springer, vol. 22(1), pages 191-221, March.
    16. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    17. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    2. Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    3. Aït-Sahalia, Yacine & Park, Joon Y., 2016. "Bandwidth selection and asymptotic properties of local nonparametric estimators in possibly nonstationary continuous-time models," Journal of Econometrics, Elsevier, vol. 192(1), pages 119-138.
    4. Bouezmarni, Taoufik & Rombouts, Jeroen V.K., 2010. "Nonparametric density estimation for positive time series," Computational Statistics & Data Analysis, Elsevier, vol. 54(2), pages 245-261, February.
    5. Xu, Ke-Li & Phillips, Peter C. B., 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(4), pages 518-528.
    6. Christian Gourieroux & Hung T. Nguyen & Songsak Sriboonchitta, 2017. "Nonparametric estimation of a scalar diffusion model from discrete time data: a survey," Annals of Operations Research, Springer, vol. 256(2), pages 203-219, September.
    7. Bandi, Federico & Corradi, Valentina & Moloche, Guillermo, 2009. "Bandwidth selection for continuous-time Markov processes," MPRA Paper 43682, University Library of Munich, Germany.
    8. Fan, Jianqing & Fan, Yingying & Jiang, Jiancheng, 2007. "Dynamic Integration of Time- and State-Domain Methods for Volatility Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 618-631, June.
    9. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Peter C.B. Phillips & Ke-Li Xu, 2007. "Tilted Nonparametric Estimation of Volatility Functions," Cowles Foundation Discussion Papers 1612, Cowles Foundation for Research in Economics, Yale University, revised Jul 2010.
    11. Jianqing Fan & Yingying Fan & Jinchi Lv, 0. "Aggregation of Nonparametric Estimators for Volatility Matrix," Journal of Financial Econometrics, Oxford University Press, vol. 5(3), pages 321-357.
    12. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.
    13. Yamamura, Mariko & Shoji, Isao, 2010. "A nonparametric method of multi-step ahead forecasting in diffusion processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(12), pages 2408-2415.
    14. Wooyong Lee & Priscilla E. Greenwood & Nancy Heckman & Wolfgang Wefelmeyer, 2017. "Pre-averaged kernel estimators for the drift function of a diffusion process in the presence of microstructure noise," Statistical Inference for Stochastic Processes, Springer, vol. 20(2), pages 237-252, July.
    15. Chen, Qiang & Zheng, Xu & Pan, Zhiyuan, 2015. "Asymptotically distribution-free tests for the volatility function of a diffusion," Journal of Econometrics, Elsevier, vol. 184(1), pages 124-144.
    16. Gospodinov, Nikolay & Hirukawa, Masayuki, 2012. "Nonparametric estimation of scalar diffusion models of interest rates using asymmetric kernels," Journal of Empirical Finance, Elsevier, vol. 19(4), pages 595-609.
    17. repec:wyi:journl:002108 is not listed on IDEAS
    18. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    19. Kanaya, Shin, 2017. "Uniform Convergence Rates Of Kernel-Based Nonparametric Estimators For Continuous Time Diffusion Processes: A Damping Function Approach," Econometric Theory, Cambridge University Press, vol. 33(4), pages 874-914, August.
    20. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    21. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.

    More about this item

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:34:y:2018:i:04:p:896-946_00. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.