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Optimal Prediction Under Asymmetric Loss

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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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Paper provided by University of Pennsylvania Center for Analytic Research and Economics in the Social Sciences in its series CARESS Working Papres with number 97-20.

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Handle: RePEc:wop:pennca:97-20

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  1. Phillips, Peter C B, 1996. "Econometric Model Determination," Econometrica, Econometric Society, vol. 64(4), pages 763-812, July.
  2. Hansen, B.E., 1992. "Autoregressive Conditional Density Estimation," RCER Working Papers 322, University of Rochester - Center for Economic Research (RCER).
  3. Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
  4. Stockman, Alan C., 1987. "Economic theory and exchange rate forecasts," International Journal of Forecasting, Elsevier, vol. 3(1), pages 3-15.
  5. Christoffersen & Diebold, . "Further Results on Forecasting and Model Selection Under Asymmetric Loss," Home Pages _059, University of Pennsylvania.
  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. Francis X. Diebold & Robert S. Mariano, 1994. "Comparing Predictive Accuracy," NBER Technical Working Papers 0169, National Bureau of Economic Research, Inc.
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