IDEAS home Printed from https://ideas.repec.org/p/bca/bocawp/01-21.html
   My bibliography  Save this paper

A Consistent Bootstrap Test for Conditional Density Functions with Time-Dependent Data

Author

Listed:
  • Fuchun Li
  • Greg Tkacz

Abstract

This paper describes a new test for evaluating conditional density functions that remains valid when the data are time-dependent and that is therefore applicable to forecasting problems. We show that the test statistic is asymptotically distributed standard normal under the null hypothesis, and diverges to infinity when the null hypothesis is false. We use a bootstrap algorithm to approximate the distribution of the test statistic in finite samples, and show that the bootstrapped distribution converges to the asymptotic distribution in probability. A Monte Carlo simulation study reveals that the bootstrap test works well and is highly robust to the value of the smoothing parameter in the kernel density estimator. An application to inflation forecasting is also presented to demonstrate the use of the test.

Suggested Citation

  • Fuchun Li & Greg Tkacz, 2001. "A Consistent Bootstrap Test for Conditional Density Functions with Time-Dependent Data," Staff Working Papers 01-21, Bank of Canada.
    • Handle: RePEc:bca:bocawp:01-21
    as

    Download full text from publisher

    File URL: https://www.bankofcanada.ca/wp-content/uploads/2010/02/wp01-21.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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..
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. Francis X. Diebold & Todd A. Gunther & Anthony S. Tay, "undated". "Evaluating Density Forecasts," CARESS Working Papres 97-18, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
    4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    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. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
    7. Zheng, John Xu, 2000. "A Consistent Test Of Conditional Parametric Distributions," Econometric Theory, Cambridge University Press, vol. 16(5), pages 667-691, October.
    8. Pagan,Adrian & Ullah,Aman, 1999. "Nonparametric Econometrics," Cambridge Books, Cambridge University Press, number 9780521355643.
    9. Donald W. K. Andrews, 1997. "A Conditional Kolmogorov Test," Econometrica, Econometric Society, vol. 65(5), pages 1097-1128, September.
    10. Horowitz, Joel L., 1994. "Bootstrap-based critical values for the information matrix test," Journal of Econometrics, Elsevier, vol. 61(2), pages 395-411, April.
    11. Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-883, November.
    12. repec:cup:etheor:v:10:y:1994:i:2:p:316-56 is not listed on IDEAS
    13. Masry, Elias & Tjøstheim, Dag, 1995. "Nonparametric Estimation and Identification of Nonlinear ARCH Time Series Strong Convergence and Asymptotic Normality: Strong Convergence and Asymptotic Normality," Econometric Theory, Cambridge University Press, vol. 11(2), pages 258-289, February.
    14. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, 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. Corradi, Valentina & Swanson, Norman R., 2006. "Bootstrap conditional distribution tests in the presence of dynamic misspecification," Journal of Econometrics, Elsevier, vol. 133(2), pages 779-806, August.
    2. James Mitchell & Stephen G. Hall, 2005. "Evaluating, Comparing and Combining Density Forecasts Using the KLIC with an Application to the Bank of England and NIESR ‘Fan’ Charts of Inflation," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 67(s1), pages 995-1033, December.
    3. Giorgio Valente & Lucio Sarno, 2004. "Comparing the accuracy of density forecasts from competing models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 23(8), pages 541-557.
    4. Polanski, Arnold & Stoja, Evarist, 2012. "Efficient evaluation of multidimensional time-varying density forecasts, with applications to risk management," International Journal of Forecasting, Elsevier, vol. 28(2), pages 343-352.
    5. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    6. Valentina Corradi & Norman R. Swanson, 2003. "A Test for Comparing Multiple Misspecified Conditional Distributions," Departmental Working Papers 200314, Rutgers University, Department of Economics.
    7. E. Fe-Rodríguez & C. Orme, 2006. "On the sensitivity of Kernel-based Conditional Moment Tests to Unconsidered Local Alternatives," Economics Discussion Paper Series 0606, Economics, The University of Manchester.

    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. Li, Fuchun & Tkacz, Greg, 2006. "A consistent bootstrap test for conditional density functions with time-series data," Journal of Econometrics, Elsevier, vol. 133(2), pages 863-886, August.
    2. Li, Fuchun, 2007. "Testing The Parametric Specification Of The Diffusion Function In A Diffusion Process," Econometric Theory, Cambridge University Press, vol. 23(2), pages 221-250, April.
    3. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, volume 1, number 8355.
    4. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    5. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    6. Chen, Bin & Hong, Yongmiao, 2011. "Generalized spectral testing for multivariate continuous-time models," Journal of Econometrics, Elsevier, vol. 164(2), pages 268-293, October.
    7. 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.
    8. 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.
    9. repec:wyi:journl:002108 is not listed on IDEAS
    10. Cai, Lili & Swanson, Norman R., 2011. "In- and out-of-sample specification analysis of spot rate models: Further evidence for the period 1982-2008," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 743-764, September.
    11. repec:wyi:journl:002117 is not listed on IDEAS
    12. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    13. repec:wyi:journl:002142 is not listed on IDEAS
    14. Stefania D'Amico, 2005. "Density selection and combination under model ambiguity: an application to stock returns," Finance and Economics Discussion Series 2005-09, Board of Governors of the Federal Reserve System (U.S.).
    15. Kristensen, Dennis, 2004. "Estimation in two classes of semiparametric diffusion models," LSE Research Online Documents on Economics 24739, London School of Economics and Political Science, LSE Library.
    16. Altissimo, Filippo & Mele, Antonio, 2004. "Simulated nonparametric estimation of continuous time models of asset prices and returns," LSE Research Online Documents on Economics 24674, London School of Economics and Political Science, LSE Library.
    17. Teresa Corzo Santamaría & Javier Gómez Biscarri, 2005. "Nonparametric estimation of convergence of interest rates: Effects on bond pricing," Spanish Economic Review, Springer;Spanish Economic Association, vol. 7(3), pages 167-190, September.
    18. Hong, Yongmiao & Li, Haitao, 2002. "Nonparametric specification testing for continuous-time models with application to spot interest rates," SFB 373 Discussion Papers 2002,32, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    19. Bin Chen & Yongmiao Hong, 2013. "Characteristic Function-Based Testing for Multifactor Continuous-Time Markov Models via Nonparametri," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    20. Yacine Ait-Sahalia, 1998. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approach," NBER Technical Working Papers 0222, National Bureau of Economic Research, Inc.
    21. Corradi, Valentina & Swanson, Norman R., 2004. "A test for the distributional comparison of simulated and historical data," Economics Letters, Elsevier, vol. 85(2), pages 185-193, November.
    22. Patrick Saart & Jiti Gao & Nam Hyun Kim, 2014. "Semiparametric methods in nonlinear time series analysis: a selective review," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 26(1), pages 141-169, March.
    23. 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.

    More about this item

    Keywords

    Econometric and statistical methods;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E37 - Macroeconomics and Monetary Economics - - Prices, Business Fluctuations, and Cycles - - - Forecasting and Simulation: Models and Applications

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:bca:bocawp:01-21. 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: the person in charge (email available below). General contact details of provider: https://edirc.repec.org/data/bocgvca.html .

    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.