Quantiles as optimal point forecasts
Loss functions play a central role in the theory and practice of forecasting. If the loss function is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is symmetric piecewise linear, any median is an optimal point forecast. Quantiles arise as optimal point forecasts under a general class of economically relevant loss functions, which nests the asymmetric piecewise linear loss, and which we refer to as generalized piecewise linear (GPL). The level of the quantile depends on a generic asymmetry parameter which reflects the possibly distinct costs of underprediction and overprediction. Conversely, a loss function for which quantiles are optimal point forecasts is necessarily GPL. We review characterizations of this type in the work of Thomson, Saerens and Komunjer, and relate to proper scoring rules, incentive-compatible compensation schemes and quantile regression. In the empirical part of the paper, the relevance of decision theoretic guidance in the transition from a predictive distribution to a point forecast is illustrated using the Bank of England's density forecasts of United Kingdom inflation rates, and probabilistic predictions of wind energy resources in the Pacific Northwest.
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- Graham Elliott & Ivana Komunjer & Allan Timmermann, 2005.
"Biases In Macroeconomic Forecasts: Irrationality Or Asymmetric Loss?,"
CAMA Working Papers
2005-14, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
- Graham Elliott & Ivana Komunjer & Allan Timmermann, 2008. "Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss?," Journal of the European Economic Association, MIT Press, vol. 6(1), pages 122-157, 03.
- Allan Timmermann & Graham Elliott & Ivana Komunjer, 2004. "Biases in Macroeconomic Forecasts: Irrationality or Asymmetric Loss?," Econometric Society 2004 North American Summer Meetings 601, Econometric Society.
- Sean D. Campbell & Francis X. Diebold, 2002.
"Weather Forecasting for Weather Derivatives,"
Center for Financial Institutions Working Papers
02-42, Wharton School Center for Financial Institutions, University of Pennsylvania.
- Campbell, Sean D. & Diebold, Francis X., 2004. "Weather forecasting for weather derivatives," CFS Working Paper Series 2004/10, Center for Financial Studies (CFS).
- Sean D. Campbell & Francis X. Diebold, 2003. "Weather Forecasting for Weather Derivatives," NBER Working Papers 10141, National Bureau of Economic Research, Inc.
- Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
- Christoffersen & Diebold, .
"Further Results on Forecasting and Model Selection Under Asymmetric Loss,"
_059, University of Pennsylvania.
- 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.
- Maurice E. Schweitzer & Gérard P. Cachon, 2000. "Decision Bias in the Newsvendor Problem with a Known Demand Distribution: Experimental Evidence," Management Science, INFORMS, vol. 46(3), pages 404-420, March.
- repec:cup:cbooks:9780521608275 is not listed on IDEAS
- Christoffersen & Diebold, .
"Optimal Prediction Under Asymmetric Loss,"
167, 1996., University of Pennsylvania.
- Peter F. Christoffersen & Francis X. Diebold, 1997. "Optimal prediction under asymmetric loss," Working Papers 97-11, Federal Reserve Bank of Philadelphia.
- 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.
- Peter F. Christoffersen & Francis X. Diebold, 1994. "Optimal Prediction Under Asymmetric Loss," NBER Technical Working Papers 0167, National Bureau of Economic Research, Inc.
- Graham Elliott & Allan Timmermann & Ivana Komunjer, 2005. "Estimation and Testing of Forecast Rationality under Flexible Loss," Review of Economic Studies, Oxford University Press, vol. 72(4), pages 1107-1125.
- Peter F. Christoffersen & Francis X.Diebold, 2003.
"Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics,"
PIER Working Paper Archive
04-009, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
- Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
- Peter F. Christoffersen & Francis X. Diebold, 2003. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," NBER Working Papers 10009, National Bureau of Economic Research, Inc.
- Christoffersen, Peter F. & Diebold, Francis X., 2003. "Financial asset returns, direction-of-change forecasting, and volatility dynamics," CFS Working Paper Series 2004/08, Center for Financial Studies (CFS).
- Ulu, Yasemin, 2007. "Optimal prediction under LINLIN loss: Empirical evidence," International Journal of Forecasting, Elsevier, vol. 23(4), pages 707-715.
- Muller, Alfred & Scarsini, Marco & Shaked, Moshe, 2002. "The Newsvendor Game Has a Nonempty Core," Games and Economic Behavior, Elsevier, vol. 38(1), pages 118-126, January.
- Basu, Sudipta & Markov, Stanimir, 2004. "Loss function assumptions in rational expectations tests on financial analysts' earnings forecasts," Journal of Accounting and Economics, Elsevier, vol. 38(1), pages 171-203, December.
- Stefan Reichelstein, 1982.
"Incentives in Government Contracts,"
522S, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- repec:cup:cbooks:9780521845731 is not listed on IDEAS
- Patton, Andrew J. & Timmermann, Allan, 2007.
"Properties of optimal forecasts under asymmetric loss and nonlinearity,"
Journal of Econometrics,
Elsevier, vol. 140(2), pages 884-918, October.
- Allan Timmermann & Andrew Patton, 2004. "Properties of Optimal Forecasts under Asymmetric Loss and Nonlinearity," Working Papers wp04-05, Warwick Business School, Finance Group.
- R. Winkler & Javier Muñoz & José Cervera & José Bernardo & Gail Blattenberger & Joseph Kadane & Dennis Lindley & Allan Murphy & Robert Oliver & David Ríos-Insua, 1996. "Scoring rules and the evaluation of probabilities," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 5(1), pages 1-60, June.
- Thomson, William, 1979. "Eliciting production possibilities from a well-informed manager," Journal of Economic Theory, Elsevier, vol. 20(3), pages 360-380, June.
- Elliott, Graham & Timmermann, Allan, 2002.
"Optimal Forecast Combination Under General Loss Functions and Forecast Error Distributions,"
University of California at San Diego, Economics Working Paper Series
qt15r9t2q2, Department of Economics, UC San Diego.
- Elliott, Graham & Timmermann, Allan, 2004. "Optimal forecast combinations under general loss functions and forecast error distributions," Journal of Econometrics, Elsevier, vol. 122(1), pages 47-79, September.
- Michael P. Clements, 2004. "Evaluating the Bank of England Density Forecasts of Inflation," Economic Journal, Royal Economic Society, vol. 114(498), pages 844-866, October.
- James E. Matheson & Robert L. Winkler, 1976. "Scoring Rules for Continuous Probability Distributions," Management Science, INFORMS, vol. 22(10), pages 1087-1096, June.
- Kenneth C. Lichtendahl, Jr. & Robert L. Winkler, 2007. "Probability Elicitation, Scoring Rules, and Competition Among Forecasters," Management Science, INFORMS, vol. 53(11), pages 1745-1755, November.
- Tilmann Gneiting, 2008. "Editorial: Probabilistic forecasting," Journal of the Royal Statistical Society Series A, Royal Statistical Society, vol. 171(2), pages 319-321.
- Komunjer, Ivana, 2005.
"Quasi-maximum likelihood estimation for conditional quantiles,"
Journal of Econometrics,
Elsevier, vol. 128(1), pages 137-164, September.
- Komunjer, Ivana, 2002. "Quasi-Maximum Likelihood Estimation for Conditional Quantiles," Working Papers 1139, California Institute of Technology, Division of the Humanities and Social Sciences.
- Sanchez, Ismael, 2006. "Short-term prediction of wind energy production," International Journal of Forecasting, Elsevier, vol. 22(1), pages 43-56.
- Louis Eeckhoudt & Christian Gollier & Harris Schlesinger, 1995. "The Risk-Averse (and Prudent) Newsboy," Management Science, INFORMS, vol. 41(5), pages 786-794, May.
- Patton, Andrew J. & Timmermann, Allan, 2007. "Testing Forecast Optimality Under Unknown Loss," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1172-1184, December.
- Tilmann Gneiting & Fadoua Balabdaoui & Adrian E. Raftery, 2007. "Probabilistic forecasts, calibration and sharpness," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(2), pages 243-268.
- Elliott, Graham & Timmermann, Allan G, 2007.
CEPR Discussion Papers
6158, C.E.P.R. Discussion Papers.
- Diebold, Francis X & Gunther, Todd A & Tay, Anthony S, 1998. "Evaluating Density Forecasts with Applications to Financial Risk Management," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 863-83, November.
- Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-47, July.
- Gneiting, Tilmann & Raftery, Adrian E., 2007. "Strictly Proper Scoring Rules, Prediction, and Estimation," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 359-378, March.
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