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Tests of Conditional Predictive Ability

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  • Raffaella Giacomini
  • Halbert White

Abstract

We propose a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite sample properties of the estimators on which the forecasts may depend are preserved asymptotically. (ii) We accommodate conditional evaluation objectives (can we predict which forecast will be more accurate at a future date?), which nest unconditional objectives (which forecast was more accurate on average?), that have been the sole focus of previous literature. As a result of (i), our tests have several advantages: they capture the effect of estimation uncertainty on relative forecast performance, they can handle forecasts based on both nested and nonnested models, they allow the forecasts to be produced by general estimation methods, and they are easy to compute. Although both unconditional and conditional approaches are informative, conditioning can help fine-tune the forecast selection to current economic conditions. To this end, we propose a two-step decision rule that uses current information to select the best forecast for the future date of interest. We illustrate the usefulness of our approach by comparing forecasts from leading parameter-reduction methods for macroeconomic forecasting using a large number of predictors. Copyright The Econometric Society 2006.

Suggested Citation

  • Raffaella Giacomini & Halbert White, 2006. "Tests of Conditional Predictive Ability," Econometrica, Econometric Society, vol. 74(6), pages 1545-1578, November.
  • Handle: RePEc:ecm:emetrp:v:74:y:2006:i:6:p:1545-1578
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    1. Kevin D. Hoover & Stephen J. Perez, 1999. "Data mining reconsidered: encompassing and the general-to-specific approach to specification search," Econometrics Journal, Royal Economic Society, vol. 2(2), pages 167-191.
    2. Giacomini, Raffaella & Komunjer, Ivana, 2005. "Evaluation and Combination of Conditional Quantile Forecasts," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 416-431, October.
    3. Clark, Todd E. & McCracken, Michael W., 2001. "Tests of equal forecast accuracy and encompassing for nested models," Journal of Econometrics, Elsevier, vol. 105(1), pages 85-110, November.
    4. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    5. 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.
    6. White,Halbert, 1994. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521252805.
    7. West, Kenneth D. & Edison, Hali J. & Cho, Dongchul, 1993. "A utility-based comparison of some models of exchange rate volatility," Journal of International Economics, Elsevier, vol. 35(1-2), pages 23-45, August.
    8. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    9. T. S. Breusch & A. R. Pagan, 1980. "The Lagrange Multiplier Test and its Applications to Model Specification in Econometrics," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 47(1), pages 239-253.
    10. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    11. McCulloch, Robert & Rossi, Peter E., 1990. "Posterior, predictive, and utility-based approaches to testing the arbitrage pricing theory," Journal of Financial Economics, Elsevier, vol. 28(1-2), pages 7-38.
    12. Donald W. K. Andrews, 2002. "Higher-Order Improvements of a Computationally Attractive "k"-Step Bootstrap for Extremum Estimators," Econometrica, Econometric Society, vol. 70(1), pages 119-162, January.
    13. White,Halbert, 1996. "Estimation, Inference and Specification Analysis," Cambridge Books, Cambridge University Press, number 9780521574464.
    14. Bierens, Herman J, 1990. "A Consistent Conditional Moment Test of Functional Form," Econometrica, Econometric Society, vol. 58(6), pages 1443-1458, November.
    15. West, Kenneth D & McCracken, Michael W, 1998. "Regression-Based Tests of Predictive Ability," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 817-840, November.
    16. Wooldridge, Jeffrey M. & White, Halbert, 1988. "Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 4(2), pages 210-230, August.
    17. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521634809.
    18. Lopez, Jose A, 2001. "Evaluating the Predictive Accuracy of Volatility Models," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 20(2), pages 87-109, March.
    19. Stinchcombe, Maxwell B. & White, Halbert, 1998. "Consistent Specification Testing With Nuisance Parameters Present Only Under The Alternative," Econometric Theory, Cambridge University Press, vol. 14(3), pages 295-325, June.
    20. Atsushi Inoue & Lutz Kilian, 2005. "In-Sample or Out-of-Sample Tests of Predictability: Which One Should We Use?," Econometric Reviews, Taylor & Francis Journals, vol. 23(4), pages 371-402.
    21. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    22. Granger,Clive W. J., 1999. "Empirical Modeling in Economics," Cambridge Books, Cambridge University Press, number 9780521778251.
    23. Sims, Christopher A & Zha, Tao, 1998. "Bayesian Methods for Dynamic Multivariate Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 949-968, November.
    24. Chao, John & Corradi, Valentina & Swanson, Norman R., 2001. "Out-Of-Sample Tests For Granger Causality," Macroeconomic Dynamics, Cambridge University Press, vol. 5(4), pages 598-620, September.
    25. Litterman, Robert B, 1986. "Forecasting with Bayesian Vector Autoregressions-Five Years of Experience," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 25-38, January.
    26. Neil R. Ericsson, 2000. "Predictable uncertainty in economic forecasting," International Finance Discussion Papers 695, Board of Governors of the Federal Reserve System (U.S.).
    27. Francis X. Diebold & Jose A. Lopez, 1995. "Forecast evaluation and combination," Research Paper 9525, Federal Reserve Bank of New York.
    28. Mc Cracken, Michael W., 2000. "Robust out-of-sample inference," Journal of Econometrics, Elsevier, vol. 99(2), pages 195-223, December.
    29. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    30. Stock, James H & Watson, Mark W, 2002. "Macroeconomic Forecasting Using Diffusion Indexes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(2), pages 147-162, April.
    31. Fisher, Franklin M, 1970. "Tests of Equality Between Sets of Coefficients in Two Linear Regressions: An Expository Note," Econometrica, Econometric Society, vol. 38(2), pages 361-366, March.
    32. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423.
    33. Harvey, David & Leybourne, Stephen & Newbold, Paul, 1997. "Testing the equality of prediction mean squared errors," International Journal of Forecasting, Elsevier, vol. 13(2), pages 281-291, June.
    34. Fama, Eugene F & MacBeth, James D, 1973. "Risk, Return, and Equilibrium: Empirical Tests," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 607-636, May-June.
    35. Corradi, Valentina & Swanson, Norman R. & Olivetti, Claudia, 2001. "Predictive ability with cointegrated variables," Journal of Econometrics, Elsevier, vol. 104(2), pages 315-358, September.
    36. Granger,Clive W. J., 1999. "Empirical Modeling in Economics," Cambridge Books, Cambridge University Press, number 9780521662086.
    37. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    38. Litterman, Robert, 1986. "Forecasting with Bayesian vector autoregressions -- Five years of experience : Robert B. Litterman, Journal of Business and Economic Statistics 4 (1986) 25-38," International Journal of Forecasting, Elsevier, vol. 2(4), pages 497-498.
    39. Leitch, Gordon & Tanner, J Ernest, 1991. "Economic Forecast Evaluation: Profits versus the Conventional Error Measures," American Economic Review, American Economic Association, vol. 81(3), pages 580-590, June.
    40. Gonedes, Nicholas J., 1973. "Evidence on the Information Content of Accounting Numbers: Accounting-based and Market-based Estimates of Systematic Risk," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 8(3), pages 407-443, June.
    41. Michael P. Clements & David F. Hendry, 2001. "Forecasting Non-Stationary Economic Time Series," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262531895, December.
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    JEL classification:

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

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