Quantiles as optimal point forecasts
AbstractLoss 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.
Bibliographic InfoArticle provided by Elsevier in its journal International Journal of Forecasting.
Volume (Year): 27 (2011)
Issue (Month): 2 ()
Contact details of provider:
Web page: http://www.elsevier.com/locate/ijforecast
Decision making; Density forecasts; Incentive-compatible compensation scheme; Loss function; Piecewise linear; Proper scoring rule; Quantile;
You can help add them by filling out this form.
CitEc Project, subscribe to its RSS feed for this item.
- Reason Lesego Machete, 2011. "Early Warning with Calibrated and Sharper Probabilistic Forecasts," Papers 1112.6390, arXiv.org, revised Jan 2012.
- Georgios Anastasiades & Patrick McSharry, 2013. "Quantile Forecasting of Wind Power Using Variability Indices," Energies, MDPI, Open Access Journal, vol. 6(2), pages 662-695, February.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).
If references are entirely missing, you can add them using this form.