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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 it numerically in less tractable cases. A key theme is that the conditionally optimal forecast is biased under asymmetric loss and that the conditionally optimal amount of bias is time-varying in general and depends on higher-order conditional moments. Thus, for example, volatility dynamics (e.g., GARCH effects) are relevant for optimal point prediction under asymmetric loss. More generally, even for models with linear conditional-mean structure, the optimal point predictor is in general nonlinear under asymmetric loss, which provides a link with the broader nonlinear time series literature.

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Bibliographic Info

Paper provided by Federal Reserve Bank of Philadelphia in its series Working Papers with number 97-11.

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Date of creation: 1997
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Handle: RePEc:fip:fedpwp:97-11

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Keywords: Forecasting;

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  1. Peter F. Christoffersen & Francis X. Diebold, 1997. "Optimal prediction under asymmetric loss," Working Papers 97-11, Federal Reserve Bank of Philadelphia.
  2. 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.
  3. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  4. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  5. Stockman, Alan C., 1987. "Economic theory and exchange rate forecasts," International Journal of Forecasting, Elsevier, vol. 3(1), pages 3-15.
  6. 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.
  7. 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.
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