Title: Forecast evaluations under asymmetric loss functions
Authors: Pin Ng - Northern Ariziona University (United States) [presenting]
Zhijie Xiao - Boston College (United States)
Kemal Guler - Anadolu University (Turkey)
Abstract: Forecasts are pervasive in all areas of applications in business and daily life. Hence evaluating the accuracy of a forecast is important for both the generators and consumers of forecasts. On measuring the accuracy of a past forecast, the aim is to illustrate that the summary statistics used should match the loss function that was used to generate the forecast. If there is strong evidence that an asymmetric loss function has been used in the generation of a forecast, then a summary statistic that corresponds to that asymmetric loss function should be used in assessing the accuracy of the forecast instead of the popular root mean square error or mean absolute error. On testing the optimality of the forecasts, it is demonstrated how the quantile regressions set in the prediction-realization framework of Mincer and Zarnowitz can be used to recover the unknown parameter that controls the potentially asymmetric loss function used in generating the past forecasts. Finally, the prediction-realization framework is applied to the Federal Reserves economic growth forecast and forecast sharing in a PC manufacturing supply chain. It is found that the Federal Reserve values overprediction approximately 1.5 times more costly than underprediction. It is also found that the PC manufacturer weighs positive forecast errors (under forecasts) about four times as costly as negative forecast errors (over forecasts).