The coefficients of correlation and determination as measures of performance in forecast verification

Abstract

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 (ie 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.