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Scanning Multivariate Conditional Densities with Probability Integral Transforms

  • Isao Ishida

    (Graduate School of Public Policy and Faculty of Economics, University of Tokyo)

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 Center for Advanced Research in Finance, Faculty of Economics, The University of Tokyo in its series CARF F-Series with number CARF-F-045.

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Length: 28 pages
Date of creation: Sep 2005
Date of revision:
Handle: RePEc:cfi:fseres:cf045
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  1. Anderson, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Labys, Paul, 2002. "Modeling and Forecasting Realized Volatility," Working Papers 02-12, Duke University, Department of Economics.
  2. BAUWENS , Luc & GIOT, Pierre & GRAMMIG, Joachim & VEREDAS, David, 2000. "A comparison of financial duration models via density forecasts," CORE Discussion Papers 2000060, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. 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.
  4. 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.
  5. Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  6. 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 863-83, November.
  7. 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.
  8. Rosenberg, Joshua V. & Engle, Robert F., 2002. "Empirical pricing kernels," Journal of Financial Economics, Elsevier, vol. 64(3), pages 341-372, June.
  9. 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.
  10. 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.
  11. 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.
  12. Jushan Bai, 2003. "Testing Parametric Conditional Distributions of Dynamic Models," The Review of Economics and Statistics, MIT Press, vol. 85(3), pages 531-549, August.
  13. Tim Bollerslev, 1986. "Generalized autoregressive conditional heteroskedasticity," EERI Research Paper Series EERI RP 1986/01, Economics and Econometrics Research Institute (EERI), Brussels.
  14. 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.
  15. 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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