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Optimal Prediction Under Asymmetric Loss

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  • Christoffersen, Peter F.
  • Diebold, Francis X.

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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Bibliographic Info

Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 13 (1997)
Issue (Month): 06 (December)
Pages: 808-817

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Handle: RePEc:cup:etheor:v:13:y:1997:i:06:p:808-817_00

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References

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  1. 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.
  2. 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.
  3. Stockman, Alan C., 1987. "Economic theory and exchange rate forecasts," International Journal of Forecasting, Elsevier, vol. 3(1), pages 3-15.
  4. Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
  5. 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.
  6. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  7. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
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