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Optimal Forecast Combinations Under General Loss Functions and Forecast Error Distributions

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Author Info
Graham Elliott
Allan Timmermann

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Abstract

Existing results on the properties and performance of forecast combinations have been derived in the context of mean squared error loss. Under this loss function empirical studies have generally found that estimates of optimal forecast combination weights lead to higher losses than equally-weighted combined forecasts which in turn outperform the best individual predictions. We show that this and other results can be overturned when asymmetries are introduced in the loss function and the forecast error distribution is skewed. We characterize the optimal combination weights for the most commonly used alternatives to mean squared error loss and demonstrate how the degree of asymmetry in the loss function and skews in the underlying forecast error distribution can significantly change the optimal combination weights. We also propose estimation methods and investigate their small sample properties in simulations and in an inflation forecasting exercise.

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Paper provided by Department of Economics, UC San Diego in its series University of California at San Diego, Economics Working Paper Series with number 2002-08.

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Date of creation: May 2002
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Handle: RePEc:cdl:ucsdec:2002-08

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  1. Valentina Corradi & Norman Swanson, 2004. "Bootstrap Procedures for Recursive Estimation Schemes With Applications to Forecast Model Selection," Departmental Working Papers 200418, Rutgers University, Department of Economics. [Downloadable!]
  2. Raffaella Giacomini & Ivana Komunjer, 2003. "Evaluation and Combination of Conditional Quantile Forecasts," Boston College Working Papers in Economics 571, Boston College Department of Economics. [Downloadable!]
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  3. Todd E. Clark & Michael W. McCracken, 2004. "Improving forecast accuracy by combining recursive and rolling forecasts," Research Working Paper RWP 04-10, Federal Reserve Bank of Kansas City. [Downloadable!]
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  4. Luiz Renato Lima & João Victor Issler, 2008. "A Panel Data Approach to Economic Forecasting: The Bias-Corrected Average Forecast," Economics Working Papers (Ensaios Economicos da EPGE) 668, Graduate School of Economics, Getulio Vargas Foundation (Brazil). [Downloadable!]
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  5. Massimo Guidolin & Carrie Fangzhou Na, 2007. "The economic and statistical value of forecast combinations under regime switching: an application to predictable U.S. returns," Working Papers 2006-059, Federal Reserve Bank of St. Louis. [Downloadable!]
  6. Eklund, Jana & Karlsson, Sune, 2005. "Forecast Combination and Model Averaging using Predictive Measures," Working Paper Series 191, Sveriges Riksbank (Central Bank of Sweden). [Downloadable!]
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  7. Heather M. Anderson & Farshid Vahid, 2003. "Nonlinear Correlograms and Partial Autocorrelograms," Monash Econometrics and Business Statistics Working Papers 19/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
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  8. 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!]
  9. Timmermann, Allan G, 2005. "Forecast Combinations," CEPR Discussion Papers 5361, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
  10. Aiolfi, Marco & Favero, Carlo A, 2003. "Model Uncertainty, Thick Modelling and the Predictability of Stock Returns," CEPR Discussion Papers 3997, C.E.P.R. Discussion Papers. [Downloadable!] (restricted)
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  11. Sancetta, A., 2007. "Online Forecast Combination for Dependent Heterogeneous Data," Cambridge Working Papers in Economics 0718, Faculty of Economics, University of Cambridge. [Downloadable!]
  12. John W. Galbraith & Greg Tkacz, 2007. "How Far Can Forecasting Models Forecast? Forecast Content Horizons for Some Important Macroeconomic Variables," Working Papers 07-1, Bank of Canada. [Downloadable!]
  13. Carlos Carmona, 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 2005-05, Department of Economics, UC San Diego. [Downloadable!]
  14. Norman Swanson & Valentina Corradi, 2006. "Nonparametric Bootstrap Procedures for Predictive Inference Based on Recursive Estimation Schemes," Departmental Working Papers 200618, Rutgers University, Department of Economics. [Downloadable!]
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  15. Sancetta, A. & Satchell, S.E., 2004. "Cost of Capital and Regulator’s Preferences: Investigation into a new method of estimating regulatory bias," Cambridge Working Papers in Economics 0441, Faculty of Economics, University of Cambridge. [Downloadable!]
  16. Todd E. Clark & Michael W. McCracken, 2006. "Combining forecasts from nested models," Research Working Paper RWP 06-02, Federal Reserve Bank of Kansas City. [Downloadable!]
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  17. Jan J. J. Groen & George Kapetanios, 2008. "Revisiting useful approaches to data-rich macroeconomic forecasting," Staff Reports 327, Federal Reserve Bank of New York. [Downloadable!]
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  18. Xiaohong Chen & Yanqin Fan, 2004. "Estimation and Model Selection of Semiparametric Copula-Based Multivariate Dynamic Models under Copula Misspecification," Working Papers 0419, Department of Economics, Vanderbilt University, revised Sep 2004. [Downloadable!]
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