THE COEFFICIENTS OF CORRELATION AND DETERMINATION AS MEASURES OF PERFORMANCE IN FORECAST VERIFICATION

This paper is concerned with the use of the coefficient of correlation (CoC) and the coefficient of determination (CoD) as performance measu res in forecast verification. Aspects of forecasting performance that are measured-and not measured (i.e., ignored)-by these coefficients ar e identified. Decompositions of familiar quadratic measures of accurac y and skill are used to explore differences between these quadratic me asures and the coefficients of correlation and determination. A linear regression model, in which forecasts are regressed on observations, i s introduced to provide insight into the interpretations of the CoC an d the CoD in this context. Issues related to the use of these coeffici ents as verification measures are discussed, including the deficiencie s inherent in one-dimensional measures of overall performance, the pro s and cons of quadratic measures of accuracy and skill vis-a-vis the c oefficients of correlation and determination, and the relative merits of the CoC and the CoD. These coefficients by themselves do not provid e an adequate basis for drawing firm conclusions regarding absolute or relative forecasting performance.