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Forecast Rationality Tests Based on Multi-Horizon Bounds

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  • Timmermann, Allan
  • Patton, Andrew

Abstract

Forecast rationality under squared error loss implies various bounds on second moments of the data across forecast horizons. For example, the mean squared forecast error should be increasing in the horizon, and the mean squared forecast should be decreasing in the horizon. We propose rationality tests based on these restrictions, including new ones that can be conducted without data on the target variable, and implement them via tests of inequality constraints in a regression framework. A new optimal revision test based on a regression of the target variable on the long-horizon forecast and the sequence of interim forecast revisions is also proposed. The size and power of the new tests are compared with those of extant tests through Monte Carlo simulations. An empirical application to the Federal Reserve's Greenbook forecasts is presented.

Suggested Citation

  • Timmermann, Allan & Patton, Andrew, 2011. "Forecast Rationality Tests Based on Multi-Horizon Bounds," CEPR Discussion Papers 8194, C.E.P.R. Discussion Papers.
    • Handle: RePEc:cpr:ceprdp:8194
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    1. Jacob A. Mincer & Victor Zarnowitz, 1969. "The Evaluation of Economic Forecasts," NBER Chapters, in: Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance, pages 3-46, National Bureau of Economic Research, Inc.
    2. Pesaran, M. Hashem & Weale, Martin, 2006. "Survey Expectations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 14, pages 715-776, Elsevier.
    3. Croushore, Dean & Stark, Tom, 2001. "A real-time data set for macroeconomists," Journal of Econometrics, Elsevier, vol. 105(1), pages 111-130, November.
    4. West, Kenneth D, 1996. "Asymptotic Inference about Predictive Ability," Econometrica, Econometric Society, vol. 64(5), pages 1067-1084, September.
    5. Hansen, Peter Reinhard, 2005. "A Test for Superior Predictive Ability," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 365-380, October.
    6. Andrew J. Patton & Allan Timmermann, 2011. "Predictability of Output Growth and Inflation: A Multi-Horizon Survey Approach," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 397-410, July.
    7. Marcellino, Massimiliano & Stock, James H. & Watson, Mark W., 2006. "A comparison of direct and iterated multistep AR methods for forecasting macroeconomic time series," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 499-526.
    8. Gultekin Isiklar & Kajal Lahiri & Prakash Loungani, 2006. "How quickly do forecasters incorporate news? Evidence from cross‐country surveys," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(6), pages 703-725, September.
    9. Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 72(4), pages 1107-1125.
    10. Clive W.J. Granger, 1999. "Outline of forecast theory using generalized cost functions," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 161-173.
    11. Stark, Tom & Croushore, Dean, 2002. "Forecasting with a real-time data set for macroeconomists," Journal of Macroeconomics, Elsevier, vol. 24(4), pages 507-531, December.
    12. Faust, Jon & Wright, Jonathan H., 2009. "Comparing Greenbook and Reduced Form Forecasts Using a Large Realtime Dataset," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 468-479.
    13. Davies, Anthony & Lahiri, Kajal, 1995. "A new framework for analyzing survey forecasts using three-dimensional panel data," Journal of Econometrics, Elsevier, vol. 68(1), pages 205-227, July.
    14. Pesaran, M. Hashem, 1989. "Consistency of short-term and long-term expectations," Journal of International Money and Finance, Elsevier, vol. 8(4), pages 511-516, December.
    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. Croushore, Dean, 2006. "Forecasting with Real-Time Macroeconomic Data," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 17, pages 961-982, Elsevier.
    17. 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.
    18. Clements,Michael & Hendry,David, 1998. "Forecasting Economic Time Series," Cambridge Books, Cambridge University Press, number 9780521632423.
    19. Patton, Andrew J. & Timmermann, Allan, 2007. "Testing Forecast Optimality Under Unknown Loss," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1172-1184, December.
    20. Nordhaus, William D, 1987. "Forecasting Efficiency: Concepts and Applications," The Review of Economics and Statistics, MIT Press, vol. 69(4), pages 667-674, November.
    21. Wolak, Frank A., 1989. "Testing inequality constraints in linear econometric models," Journal of Econometrics, Elsevier, vol. 41(2), pages 205-235, June.
    22. Corradi, Valentina & Fernandez, Andres & Swanson, Norman R., 2009. "Information in the Revision Process of Real-Time Datasets," Journal of Business & Economic Statistics, American Statistical Association, vol. 27(4), pages 455-467.
    23. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    24. Patton, Andrew J. & Timmermann, Allan, 2007. "Properties of optimal forecasts under asymmetric loss and nonlinearity," Journal of Econometrics, Elsevier, vol. 140(2), pages 884-918, October.
    25. Moon, Hyungsik Roger & Schorfheide, Frank, 2009. "Estimation with overidentifying inequality moment conditions," Journal of Econometrics, Elsevier, vol. 153(2), pages 136-154, December.
    26. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    27. Capistrán Carlos, 2007. "Optimality Tests for Multi-Horizon Forecasts," Working Papers 2007-14, Banco de México.
    28. Faust, Jon & Wright, Jonathan H., 2008. "Efficient forecast tests for conditional policy forecasts," Journal of Econometrics, Elsevier, vol. 146(2), pages 293-303, October.
    29. Schmidt, Peter, 1974. "The Asymptotic Distribution of Forecasts in the Dynamic Simulation of an Econometric Model," Econometrica, Econometric Society, vol. 42(2), pages 303-309, March.
    30. Patton, Andrew J. & Timmermann, Allan, 2010. "Why do forecasters disagree? Lessons from the term structure of cross-sectional dispersion," Journal of Monetary Economics, Elsevier, vol. 57(7), pages 803-820, October.
    31. Francis X. Diebold & Glenn D. Rudebusch, 1989. "Forecasting output with the composite leading index: an ex ante analysis," Finance and Economics Discussion Series 90, Board of Governors of the Federal Reserve System (U.S.).
    32. Halbert White, 2000. "A Reality Check for Data Snooping," Econometrica, Econometric Society, vol. 68(5), pages 1097-1126, September.
    33. Patton, Andrew J. & Timmermann, Allan, 2010. "Monotonicity in asset returns: New tests with applications to the term structure, the CAPM, and portfolio sorts," Journal of Financial Economics, Elsevier, vol. 98(3), pages 605-625, December.
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    More about this item

    Keywords

    Forecast horizon; Forecast optimality; Real-time data; Survey forecasts;
    All these keywords.

    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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