A new basis for measuring and evaluating forecasting models

Abstract

Assume that we generate forecasts from a model y=cx+d+ξ. The constants “c” and “d” are placement parameters estimated from observations on x and y, and ξ is the residual error variable.

Our objective is to develop a method for accurately measuring and evaluating the risk profile of a forecasted variable y. To do so, it is necessary to first obtain an accurate representation of the histogram of a forecasting model's residual errors. That is not always so easy because the histogram of the residual ξ may be symmetric, or it may be skewed to either the left of or to the right of its mode. We introduce the probability density function (PDF) family of functions because it is versatile enough to fit any residual's locus be it skewed to the left, symmetric about the mean, or skewed to the right. When we have measured the residual's density, we show how to correctly calculate the risk profile of the forecasted variable y from the density of the residual using the PPD function. We achieve the desired and accurate risk profile for y that we seek. We conclude the chapter by discussing how a universally followed paradigm leads to misstating the risk profile and to wrongheaded decisions by too freely using the symmetric Gauss–normal function instead of the PPD function. We expect that this chapter will open up many new avenues of progress for econometricians.

Citation

Waage, F. (2009), "A new basis for measuring and evaluating forecasting models", Lawrence, K.D. and Klimberg, R.K. (Ed.) Advances in Business and Management Forecasting (Advances in Business and Management Forecasting, Vol. 6), Emerald Group Publishing Limited, Leeds, pp. 135-155. https://doi.org/10.1108/S1477-4070(2009)0000006009