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Scanning Multivariate Conditional Densities with Probability Integral Transforms

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Author Info
Isao Ishida (Graduate School of Public Policy and Faculty of Economics, University of Tokyo)
Abstract

This paper introduces new ways to construct probability integral transforms of random vectors that complement the approach of Diebold, Hahn, and Tay (1999) for evaluating multivariate conditional density forecasts. Our approach enables us to "scan" multivariate densities in various di.erent ways. A simple bivariate normal example is given that illustrates how "scanning" a multivariate density from particular angles leads to tests with no power or high power. An empirical example is also given that applies several di.erent probability integral transforms to specification testing of Engle's (2002) dynamic conditional correlation model for multivariate financial returns time series with multivariate normal and t errors.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-369.

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Length: 28 pages
Date of creation: Sep 2005
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Handle: RePEc:tky:fseres:2005cf369

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  1. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June. [Downloadable!] (restricted)
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  2. Raffaella Giacomini & Halbert White, 2004. "Tests of Conditional Predictive Ability," University of California at San Diego, Economics Working Paper Series 2003-09, Department of Economics, UC San Diego. [Downloadable!]
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  3. Luc Bauwens & Sébastien Laurent, 2002. "A New Class of Multivariate skew Densities, with Application to GARCH Models," Computing in Economics and Finance 2002 5, Society for Computational Economics.
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  4. Luc Bauwens & Pierre Giot & Joachim Grammig & David Veredas, 2000. "A Comparison of Financial Duration Models via Density Forecasts," Econometric Society World Congress 2000 Contributed Papers 0810, Econometric Society. [Downloadable!]
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  5. Norman Swanson & Valentina Corradi, 2004. "Predictive Density Accuracy Tests," Working Papers wp04-16, Warwick Business School, Financial Econometrics Research Centre. [Downloadable!]
  6. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August. [Downloadable!] (restricted)
  7. Francis X. Diebold & Jinyong Hahn & Anthony S. Tay, 1999. "Multivariate Density Forecast Evaluation And Calibration In Financial Risk Management: High-Frequency Returns On Foreign Exchange," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 661-673, November. [Downloadable!] (restricted)
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2003. "Modeling and Forecasting Realized Volatility," Econometrica, Econometric Society, vol. 71(2), pages 579-625, March. [Downloadable!] (restricted)
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  9. Berkowitz, Jeremy, 2001. "Testing Density Forecasts, with Applications to Risk Management," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 465-74, October.
  10. Raffaella Giacomini, 2002. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods," Boston College Working Papers in Economics 583, Boston College Department of Economics. [Downloadable!]
  11. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, 06. [Downloadable!] (restricted)
  12. Engle, Robert, 2002. "Dynamic Conditional Correlation: A Simple Class of Multivariate Generalized Autoregressive Conditional Heteroskedasticity Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 339-50, July.
  13. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
  14. Clements, Michael P. & Smith, Jeremy, 2002. "Evaluating multivariate forecast densities: a comparison of two approaches," International Journal of Forecasting, Elsevier, vol. 18(3), pages 397-407. [Downloadable!] (restricted)
  15. Raffaella Giacomini, 2002. "Comparing Density Forecasts via Weighted Likelihood Ratio Tests: Asymptotic and Bootstrap Methods," University of California at San Diego, Economics Working Paper Series 2002-12, Department of Economics, UC San Diego. [Downloadable!]
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  1. Tilmann Gneiting & Larissa Stanberry & Eric Grimit & Leonhard Held & Nicholas Johnson, 2008. "Assessing probabilistic forecasts of multivariate quantities, with an application to ensemble predictions of surface winds," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 17(2), pages 211-235, August. [Downloadable!] (restricted)
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