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Optimal Prediction Under Asymmetric Loss

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  • Peter F. Christoffersen
  • Francis X. Diebold

Abstract

Prediction problems involving asymmetric loss functions arise routinely in many fields, yet the theory of optimal prediction under asymmetric loss is not well developed. We study the optimal prediction problem under general loss structures and characterize the optimal predictor. We compute the optimal predictor analytically in two leading cases. Analytic solutions for the optimal predictor are not available in more complicated cases, so we develop numerical procedures for computing it. We illustrate the results by forecasting the GARCH(1,1) process which, although white noise, is non-trivially forecastable under asymmetric loss.

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File URL: http://www.nber.org/papers/t0167.pdf
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Bibliographic Info

Paper provided by National Bureau of Economic Research, Inc in its series NBER Technical Working Papers with number 0167.

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Date of creation: Oct 1994
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Publication status: published as as "Futher Results on Forcasting and Model Selection Under Asymmetric Loss ," Journal of Applied Econometrics, Vol. 11 (1996): 561-572.
Handle: RePEc:nbr:nberte:0167

Note: EFG CF
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Postal: National Bureau of Economic Research, 1050 Massachusetts Avenue Cambridge, MA 02138, U.S.A.
Phone: 617-868-3900
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Web page: http://www.nber.org
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  1. Peter F. Christoffersen & Francis X. Diebold, . "Optimal Prediction Under Asymmetric Loss," CARESS Working Papres 97-20, University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences.
  2. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  3. Christoffersen, Peter F & Diebold, Francis X, 1996. "Further Results on Forecasting and Model Selection under Asymmetric Loss," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 561-71, Sept.-Oct.
  4. Weiss, Andrew A, 1996. "Estimating Time Series Models Using the Relevant Cost Function," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 11(5), pages 539-60, Sept.-Oct.
  5. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-44, January.
  6. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  7. Stockman, Alan C., 1987. "Economic theory and exchange rate forecasts," International Journal of Forecasting, Elsevier, vol. 3(1), pages 3-15.
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