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

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  • 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
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. Hall, Stephen G. & Mitchell, James, 2007. "Combining density forecasts," International Journal of Forecasting, Elsevier, vol. 23(1), pages 1-13.
    3. 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.
    4. 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.
    5. 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.
    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. 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.

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    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

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