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Properties of Optimal Forecasts

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  • Patton, Andrew J
  • Timmermann, Allan G

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 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 non-linear 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 sub-optimality 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 new results on forecast error properties that may be tested when the forecaster's loss function is unknown but restrictions can be imposed on the data-generating process, 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.

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Bibliographic Info

Paper provided by C.E.P.R. Discussion Papers in its series CEPR Discussion Papers with number 4037.

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Date of creation: Aug 2003
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Handle: RePEc:cpr:ceprdp:4037

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Keywords: efficient markets; forecast evaluation; loss function; rationality;

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References

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Citations

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Cited by:
  1. Pablo Pincheira, 2006. "Shrinkage Based Tests of the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 376, Central Bank of Chile.
  2. Anatolyev, Stanislav, 2009. "Dynamic modeling under linear-exponential loss," Economic Modelling, Elsevier, vol. 26(1), pages 82-89, January.
  3. 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.
  4. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
  5. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production and Sales with Automated Procedures," Computing in Economics and Finance 2004 112, Society for Computational Economics.
  6. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  7. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
  8. Timmermann, Allan G, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers.
  9. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production with Automated Procedures," Econometric Society 2004 Latin American Meetings 177, Econometric Society.
  10. Carlos Capistrán & Gabriel López-Moctezuma, 2008. "Experts´ Macroeconomics Expectations: An Evaluation of Mexican Short-Run Forecasts," Working Papers 2008-11, Banco de México.
  11. 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.
  12. Andrew J. Patton & Allan Timmermann, 2005. "Testable Implications of Forecast Optimality," STICERD - Econometrics Paper Series /2005/485, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.

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