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Evaluating Density Forecasts via the Copula Approach

Author

Listed:
  • Xiaohong Chen

    () (Department of Economics, New York University)

  • Yanqin Fan

    () (Department of Ecomomics, Vanderbilt University)

Abstract

In this paper, we develop a general approach for constructing simple tests for the correct density forecasts, or equivalently, for i.i.d. uniformity of appropriately transformed random variables. It is based on nesting a series of i.i.d. uniform random variables into a class of copula-based stationary Markov processes. As such, it can be used to test for i.i.d. uniformity against alternative processes that exhibit a wide variety of marginal properties and temporal dependence properties, including skewed and fat-tailed marginal distributions, asymmetric dependence, and positive tail dependence. In addition, we develop tests for the dependence structure of the forecasting model that are robust to possible misspecification of the marginal distribution.

Suggested Citation

  • Xiaohong Chen & Yanqin Fan, 2002. "Evaluating Density Forecasts via the Copula Approach," Vanderbilt University Department of Economics Working Papers 0225, Vanderbilt University Department of Economics, revised Sep 2003.
  • Handle: RePEc:van:wpaper:0225
    as

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    File URL: http://www.accessecon.com/pubs/VUECON/vu02-w25R.pdf
    File Function: Revised version, 2003
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    References listed on IDEAS

    as
    1. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    2. P. Gagliardini & C. Gourieroux, 2008. "Duration time-series models with proportional hazard," Journal of Time Series Analysis, Wiley Blackwell, vol. 29(1), pages 74-124, January.
    3. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
    4. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-474, October.
    5. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Density forecasts; Gaussian copula; probability integral transform; nonlinear time series;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods

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