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Properties of Optimal Forecasts

Author

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  • Allan Timmermann
  • Andrew J. Patton

Abstract

Evaluation of forecast optimality in economics and finance has almost exclusively been conducted under the assumption of mean squared error loss. Under this loss function optimal forecasts should be unbiased and forecast errors should be serially uncorrelated at the single period horizon with increasing variance as the forecast horizon grows. Using analytical results, we show in this paper that all the standard properties of optimal forecasts can be invalid under asymmetric loss and nonlinear data generating processes and thus may be very misleading as a benchmark for an optimal forecast. Our theoretical results suggest that many of the conclusions in the empirical literature concerning suboptimality of forecasts could be premature. We extend the properties that an optimal forecast should have to a more general setting than previously considered in the literature. We also present results on forecast error properties that may be tested when the forecaster's loss function is unknown, and introduce a change of measure, following which the optimum forecast errors for general loss functions have the same properties as optimum errors under MSE loss

Suggested Citation

  • Allan Timmermann & Andrew J. Patton, 2004. "Properties of Optimal Forecasts," Econometric Society 2004 North American Winter Meetings 234, Econometric Society.
  • Handle: RePEc:ecm:nawm04:234
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    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production with Automated Procedures," Econometric Society 2004 Latin American Meetings 177, Econometric Society.
    2. Carlos Capistrán & Gabriel López-Moctezuma, 2008. "Experts´ Macroeconomics Expectations: An Evaluation of Mexican Short-Run Forecasts," Working Papers 2008-11, Banco de México.
    3. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    4. Rómulo Chumacero E., 2004. "Forecasting Chilean Industrial Production and Sales With Automated Procedures," Journal Economía Chilena (The Chilean Economy), Central Bank of Chile, vol. 7(3), pages 47-56, December.
    5. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
    6. Anatolyev, Stanislav, 2009. "Dynamic modeling under linear-exponential loss," Economic Modelling, Elsevier, vol. 26(1), pages 82-89, January.
    7. Gonzalez-Rivera, Gloria & Lee, Tae-Hwy & Mishra, Santosh, 2004. "Forecasting volatility: A reality check based on option pricing, utility function, value-at-risk, and predictive likelihood," International Journal of Forecasting, Elsevier, vol. 20(4), pages 629-645.
    8. Capistrán, Carlos, 2008. "Bias in Federal Reserve inflation forecasts: Is the Federal Reserve irrational or just cautious?," Journal of Monetary Economics, Elsevier, vol. 55(8), pages 1415-1427, November.
    9. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 4, pages 135-196, Elsevier.
    10. repec:zbw:cfswop:wp200508 is not listed on IDEAS
    11. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    12. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    13. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.

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    More about this item

    Keywords

    forecast evaluation; loss function; rationality; efficient markets;
    All these keywords.

    JEL classification:

    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • 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

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