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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. Timmermann, Allan, 2006. "Forecast Combinations," Handbook of Economic Forecasting, Elsevier.
  2. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney.
  3. Carlos Capistrán & Gabriel López-Moctezuma, 2008. "Experts´ Macroeconomics Expectations: An Evaluation of Mexican Short-Run Forecasts," Working Papers 2008-11, Banco de México.
  4. McCracken, Michael W., 2007. "Asymptotics for out of sample tests of Granger causality," Journal of Econometrics, Elsevier, vol. 140(2), pages 719-752, October.
  5. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production with Automated Procedures," Econometric Society 2004 Latin American Meetings 177, Econometric Society.
  6. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers.
  7. Carmona, Carlos Capistran, 2005. "Bias in Federal Reserve Inflation Forecasts: Is the Federal Reserve Irrational or Just Cautious?," University of California at San Diego, Economics Working Paper Series qt6v28v0b6, Department of Economics, UC San Diego.
  8. Rómulo Chumacero, 2004. "Forecasting Chilean Industrial Production and Sales with Automated Procedures," Working Papers Central Bank of Chile 260, Central Bank of Chile.
  9. Andrew J. Patton & Allan Timmermann, 2005. "Testable implications of forecast optimality," LSE Research Online Documents on Economics 6834, London School of Economics and Political Science, LSE Library.
  10. 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.
  11. Anatolyev, Stanislav, 2009. "Dynamic modeling under linear-exponential loss," Economic Modelling, Elsevier, vol. 26(1), pages 82-89, January.

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