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 measures in forecast verification. Aspects of forecasting performance that are measured—and not measured (i.e., ignored)—by these coefficients are identified. Decompositions of familiar quadratic measures of accuracy and skill are used to explore differences between these quadratic measures and the coefficients of correlation and determination. A linear regression model, in which forecasts are regressed on observations, is introduced to provide insight into the interpretations of the CoC and the CoD in this context. Issues related to the use of these coefficients as verification measures are discussed, including the deficiencies inherent in one-dimensional measures of overall performance, the pros and cons of quadratic measures of accuracy and skill vis-à-vis the coefficients of correlation and determination, and the relative merits of the CoC and the CoD. These coefficients by themselves do not provide an adequate basis for drawing firm conclusions regarding absolute or relative forecasting performance.