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Properties of Optimal Forecasts

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Author Info
Patton, Andrew J
Timmermann, Allan G

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

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing
C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Other Model Applications

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References listed on IDEAS
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Carlos Capistrán-Carmona, 2005. "Bias in Federal Reserve Inflation Forecasts: Is the Federal Reserve Irrational or Just Cautious?," Computing in Economics and Finance 2005 127, Society for Computational Economics. [Downloadable!]
    Other versions:
  2. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production with Automated Procedures," Econometric Society 2004 Latin American Meetings 177, Econometric Society. [Downloadable!]
  3. Stanislav Anatolyev, 2006. "Dynamic modeling under linear-exponential loss," Working Papers w0092, Center for Economic and Financial Research (CEFIR). [Downloadable!]
    Other versions:
  4. Romulo A. Chumacero, 2004. "Forecasting Chilean Industrial Production and Sales with Automated Procedures," Computing in Economics and Finance 2004 112, Society for Computational Economics. [Downloadable!]
    Other versions:
  5. Andrew Patton, 2006. "Volatility Forecast Comparison using Imperfect Volatility Proxies," Research Paper Series 175, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
  6. 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. [Downloadable!]
  7. Graham Elliott & Ivana Komunjer & Allan Timmermann, 2005. "Biases In Macroeconomic Forecasts: Irrationality Or Asymmetric Loss?," CAMA Working Papers 2005-14, Australian National University, Centre for Applied Macroeconomic Analysis. [Downloadable!]
    Other versions:
  8. Pablo Pincheira, 2006. "Shrinkage Based Tests of the Martingale Difference Hypothesis," Working Papers Central Bank of Chile 376, Central Bank of Chile. [Downloadable!]
  9. Elliott, Graham & Komunjer, Ivana & Timmermann, Allan G, 2003. "Estimating Loss Function Parameters," CEPR Discussion Papers 3821, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  10. Timmermann, Allan G, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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