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Evaluation and Combination of Conditional Quantile Forecasts

  • Giacomini, Raffaella
  • Komunjer, Ivana

This paper proposes a method for comparing and combining conditional quantile forecasts based on the principle of 'encompassing'. Our test for conditional quantile forecast encompassing (CQFE) is a test of superior predictive ability, constructed as a Wald-type test on the coefficients of an optimal combination of alternative forecasts. The CQFE test is a 'model free' test that can be used to compare any given number of alternative forecasts, and is relatively easy to implement by GMM techniques appropriately modified to accommodate non-differentiable criterion functions. Further, our theoretical framework provides a basis for combining quantile forecasts, when neither forecast has superior predictive ability. A central feature of our method is the focus on conditional, rather than unconditional expected loss in the formulation of the encompassing test, which links our approach to Christoffersen's (1998) 'conditional coverage' test for evaluation of quantile forecasts. An empirical application to the problem of Value at Risk evaluation illustrates the usefulness of the proposed techniques.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number qt4n99t4wz.

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Date of creation: 01 Jun 2002
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Handle: RePEc:cdl:ucsdec:qt4n99t4wz
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  1. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809, June.
  2. James Taylor & Derek Bunn, 1998. "Combining forecast quantiles using quantile regression: Investigating the derived weights, estimator bias and imposing constraints," Journal of Applied Statistics, Taylor & Francis Journals, vol. 25(2), pages 193-206.
  3. Zheng, John Xu, 1998. "A Consistent Nonparametric Test Of Parametric Regression Models Under Conditional Quantile Restrictions," Econometric Theory, Cambridge University Press, vol. 14(01), pages 123-138, February.
  4. Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
  5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
  6. James H. Stock & Mark W. Watson, 1991. "A simple estimator of cointegrating vectors in higher order integrated systems," Working Paper Series, Macroeconomic Issues 91-3, Federal Reserve Bank of Chicago.
  7. Raffaella Giacomini & Halbert White, 2003. "Tests of conditional predictive ability," Boston College Working Papers in Economics 572, Boston College Department of Economics.
  8. Peter Christoffersen & Jinyong Hahn & Atsushi Inoue, 2001. "Testing and Comparing Value-at-Risk Measures," CIRANO Working Papers 2001s-03, CIRANO.
  9. Donald W.K. Andrews & Christopher J. Monahan, 1990. "An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," Cowles Foundation Discussion Papers 942, Cowles Foundation for Research in Economics, Yale University.
  10. Newey, W.K. & West, K.D., 1992. "Automatic Lag Selection in Covariance Matrix Estimation," Working papers 9220, Wisconsin Madison - Social Systems.
  11. McNeil, Alexander J. & Frey, Rudiger, 2000. "Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 271-300, November.
  12. Robert Engle & Simone Manganelli, 2000. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Econometric Society World Congress 2000 Contributed Papers 0841, Econometric Society.
  13. Kenneth D. West, 1995. "Another Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator," NBER Technical Working Papers 0183, National Bureau of Economic Research, Inc.
  14. Kenneth D. West, 1994. "Asymptotic Inference About Predictive Ability," Macroeconomics 9410002, EconWPA.
  15. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  16. Clemen, Robert T., 1989. "Combining forecasts: A review and annotated bibliography," International Journal of Forecasting, Elsevier, vol. 5(4), pages 559-583.
  17. James H. Stock & Mark W.Watson, 2003. "Forecasting Output and Inflation: The Role of Asset Prices," Journal of Economic Literature, American Economic Association, vol. 41(3), pages 788-829, September.
  18. Kenneth D. West, 2000. "Encompassing Tests When No Model Is Encompassing," NBER Technical Working Papers 0256, National Bureau of Economic Research, Inc.
  19. Len Umantsev & Victor Chernozhukov, 2001. "Conditional value-at-risk: Aspects of modeling and estimation," Empirical Economics, Springer, vol. 26(1), pages 271-292.
  20. Donald W.K. Andrews, 1988. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Cowles Foundation Discussion Papers 877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
  21. Martin S. Eichenbaum & Lars Peter Hansen & Kenneth J. Singleton, 1988. "A Time Series Analysis of Representative Agent Models of Consumption and Leisure Choice Under Uncertainty," The Quarterly Journal of Economics, Oxford University Press, vol. 103(1), pages 51-78.
  22. Herman J. Bierens & Donna K. Ginther, 2001. "Integrated Conditional Moment testing of quantile regression models," Empirical Economics, Springer, vol. 26(1), pages 307-324.
  23. Francis X. Diebold, 1989. "Forecast combination and encompassing: reconciling two divergent literatures," Finance and Economics Discussion Series 80, Board of Governors of the Federal Reserve System (U.S.).
  24. Koenker, Roger & Zhao, Quanshui, 1996. "Conditional Quantile Estimation and Inference for Arch Models," Econometric Theory, Cambridge University Press, vol. 12(05), pages 793-813, December.
  25. Yuichi Kitamura & Michael Stutzer, 1997. "An Information-Theoretic Alternative to Generalized Method of Moments Estimation," Econometrica, Econometric Society, vol. 65(4), pages 861-874, July.
  26. Wouter J. Den Haan & Andrew Levin, 1996. "Inferences from Parametric and Non-Parametric Covariance Matrix Estimation Procedures," NBER Technical Working Papers 0195, National Bureau of Economic Research, Inc.
  27. HENRY, David F. & RICHARD, Jean-François, . "On the formulation of empirical models in dynamic econometrics," CORE Discussion Papers RP 502, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  28. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  29. James H. Stock & Mark W. Watson, 1998. "A Comparison of Linear and Nonlinear Univariate Models for Forecasting Macroeconomic Time Series," NBER Working Papers 6607, National Bureau of Economic Research, Inc.
  30. Mizon, Grayham E & Richard, Jean-Francois, 1986. "The Encompassing Principle and Its Application to Testing Non-nested Hypotheses," Econometrica, Econometric Society, vol. 54(3), pages 657-78, May.
  31. Goffe, William L. & Ferrier, Gary D. & Rogers, John, 1994. "Global optimization of statistical functions with simulated annealing," Journal of Econometrics, Elsevier, vol. 60(1-2), pages 65-99.
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  33. repec:cup:etheor:v:12:y:1996:i:5:p:793-813 is not listed on IDEAS
  34. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
  35. Hansen, Lars Peter, 1982. "Large Sample Properties of Generalized Method of Moments Estimators," Econometrica, Econometric Society, vol. 50(4), pages 1029-54, July.
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