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Forecast Rationality Tests Based on Multi-Horizon Bounds

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  • Andrew J. Patton
  • Allan Timmermann

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 test of optimal forecast revision 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

  • Andrew J. Patton & Allan Timmermann, 2011. "Forecast Rationality Tests Based on Multi-Horizon Bounds," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 30(1), pages 1-17, June.
    • Handle: RePEc:taf:jnlbes:v:30:y:2011:i:1:p:1-17
    DOI: 10.1080/07350015.2012.634337
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    Cited by:

    1. Bańbura, Marta & Giannone, Domenico & Modugno, Michele & Reichlin, Lucrezia, 2013. "Now-Casting and the Real-Time Data Flow," Handbook of Economic Forecasting, Elsevier.
    2. Thomas Jobert & Lionel Persyn, 2012. "Quelques constats sur les prévisions conjoncturelles de la croissance française," Revue d'économie politique, Dalloz, vol. 122(6), pages 833-849.
    3. Roberto Casarin, 2014. "A Note on Tractable State-Space Model for Symmetric Positive-Definite Matrices," Working Papers 2014:23, Department of Economics, University of Venice "Ca' Foscari".
    4. Lennart F. Hoogerheide & Francesco Ravazzolo & Herman K. van Dijk, 2011. "Backtesting Value-at-Risk using Forecasts for Multiple Horizons, a Comment on the Forecast Rationality Tests of A.J. Patton and A. Timmermann," Tinbergen Institute Discussion Papers 11-131/4, Tinbergen Institute.
    5. Charles Rahal, 2015. "Housing Market Forecasting with Factor Combinations," Discussion Papers 15-05r, Department of Economics, University of Birmingham.

    More about this item

    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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