IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v26y2010i02p541-563_10.html
   My bibliography  Save this article

Reweighted Functional Estimation Of Diffusion Models

Author

Listed:
  • Xu, Ke-Li

Abstract

The local linear method is popular in estimating nonparametric continuous-time diffusion models, but it may produce negative results for the diffusion (or volatility) functions and thus lead to insensible inference. We demonstrate this using U.S. interest rate data. We propose a new functional estimation method of the diffusion coefficient based on reweighting the conventional Nadaraya–Watson estimator. It preserves the appealing bias properties of the local linear estimator and is guaranteed to be nonnegative in finite samples. A limit theory is developed under mild requirements (recurrence) of the data generating mechanism without assuming stationarity or ergodicity.

Suggested Citation

  • Xu, Ke-Li, 2010. "Reweighted Functional Estimation Of Diffusion Models," Econometric Theory, Cambridge University Press, vol. 26(2), pages 541-563, April.
    • Handle: RePEc:cup:etheor:v:26:y:2010:i:02:p:541-563_10
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466609100087/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    3. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    5. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    6. Hall, Peter & Wolff, Rodney C. L. & Yao, Qiwei, 1999. "Methods for estimating a conditional distribution function," LSE Research Online Documents on Economics 6631, London School of Economics and Political Science, LSE Library.
    7. 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.
    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.
    9. Peter C. B. Phillips, 2001. "Descriptive econometrics for non-stationary time series with empirical illustrations," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 16(3), pages 389-413.
    10. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    11. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    12. Cai, Zongwu, 2001. "Weighted Nadaraya-Watson regression estimation," Statistics & Probability Letters, Elsevier, vol. 51(3), pages 307-318, February.
    13. Yongmiao Hong, 2005. "Nonparametric Specification Testing for Continuous-Time Models with Applications to Term Structure of Interest Rates," The Review of Financial Studies, Society for Financial Studies, vol. 18(1), pages 37-84.
    14. Manuel Arapis & Jiti Gao, 2006. "Empirical Comparisons in Short-Term Interest Rate Models Using Nonparametric Methods," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 310-345.
    15. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    16. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871532, September.
    17. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    18. Song Xi Chen & Yong Song Qin, 2002. "Confidence Intervals Based on Local Linear Smoother," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 29(1), pages 89-99, March.
    19. 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.
    20. 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.
    21. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    22. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    23. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521871549, September.
    24. 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.
    25. Blundell,Richard & Newey,Whitney & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692106, September.
    26. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1980. "An Analysis of Variable Rate Loan Contracts," Journal of Finance, American Finance Association, vol. 35(2), pages 389-403, May.
    27. Nicolau, João, 2003. "Bias Reduction In Nonparametric Diffusion Coefficient Estimation," Econometric Theory, Cambridge University Press, vol. 19(5), pages 754-777, October.
    28. Moloche, Guillermo, 2001. "Local Nonparametric Estimation of Scalar Diffusions," MPRA Paper 46154, University Library of Munich, Germany.
    29. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
    30. Ziegelmann, Flavio A., 2002. "Nonparametric Estimation Of Volatility Functions: The Local Exponential Estimator," Econometric Theory, Cambridge University Press, vol. 18(4), pages 985-991, August.
    31. Yu, K. & Jones, M.C., 2004. "Likelihood-Based Local Linear Estimation of the Conditional Variance Function," Journal of the American Statistical Association, American Statistical Association, vol. 99, pages 139-144, January.
    32. Darrell Duffie & Rui Kan, 1996. "A Yield‐Factor Model Of Interest Rates," Mathematical Finance, Wiley Blackwell, vol. 6(4), pages 379-406, October.
    33. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    34. Chen, Song Xi & Gao, Jiti & Tang, Chenghong, 2005. "A test for model specification of diffusion processes," MPRA Paper 11976, University Library of Munich, Germany, revised Feb 2007.
    35. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
    36. Linton, Oliver & Nielsen, Jens Perch, 1994. "A multiplicative bias reduction method for nonparametric regression," Statistics & Probability Letters, Elsevier, vol. 19(3), pages 181-187, February.
    37. Durham, Garland B., 2003. "Likelihood-based specification analysis of continuous-time models of the short-term interest rate," Journal of Financial Economics, Elsevier, vol. 70(3), pages 463-487, December.
    38. Blundell,Richard & Newey,Whitney K. & Persson,Torsten (ed.), 2007. "Advances in Economics and Econometrics," Cambridge Books, Cambridge University Press, number 9780521692090, September.
    39. 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.
    40. P. Hall & B. Presnell, 1999. "Intentionally biased bootstrap methods," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(1), pages 143-158.
    41. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    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. 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.
    2. Ye, Xu-Guo & Lin, Jin-Guan & Zhao, Yan-Yong & Hao, Hong-Xia, 2015. "Two-step estimation of the volatility functions in diffusion models with empirical applications," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 135-159.
    3. 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.
    4. Ke-Li Xu & Peter C. B. Phillips, 2011. "Tilted Nonparametric Estimation of Volatility Functions With Empirical Applications," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(4), pages 518-528, October.
    5. Xiong, Xianzhu & Ou, Meijuan & Chen, Ailian, 2021. "Reweighted Nadaraya–Watson estimation of conditional density function in the right-censored model," Statistics & Probability Letters, Elsevier, vol. 168(C).
    6. Muhammad Hanif, 2011. "Reweighted Nadaraya-Watson estimator of scalar diffusion models by using asymmetric kernels," Far East Journal of Psychology and Business, Far East Research Centre, vol. 4(5), pages 53-69, July.
    7. 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.
    8. Yunyan Wang & Lixin Zhang & Mingtian Tang, 2012. "Re-weighted functional estimation of second-order diffusion processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 75(8), pages 1129-1151, November.

    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. 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.
    2. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    3. repec:wyi:journl:002108 is not listed on IDEAS
    4. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    5. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    6. 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.
    7. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    8. 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.
    9. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    10. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    11. 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.
    12. 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.
    13. Jianqing Fan, 2004. "A selective overview of nonparametric methods in financial econometrics," Papers math/0411034, arXiv.org.
    14. 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.
    15. Al-Zoubi, Haitham A., 2009. "Short-term spot rate models with nonparametric deterministic drift," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 731-747, August.
    16. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    17. 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.
    18. 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.
    19. Diep Duong & Norman Swanson, 2013. "Density and Conditional Distribution Based Specification Analysis," Departmental Working Papers 201312, Rutgers University, Department of Economics.
    20. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    21. Yu, Jun, 2012. "Bias in the estimation of the mean reversion parameter in continuous time models," Journal of Econometrics, Elsevier, vol. 169(1), pages 114-122.

    More about this item

    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:26:y:2010:i:02:p:541-563_10. 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.