## Correlation Analysis

In analyzing a model's forecast capability, the correlation between forecast and actual values is of substantial interest. The formula for the simple correlation coefficient, r, for forecast and actual values, f and x, respectively, is

fx where of is the covariance between the forecast and actual series, and Uf and ux are the sample standard deviations of the forecast and actual series, respectively. Basic spreadsheet and statistical software readily provide these data, making the calculation of r a relatively simple task. Generally speaking, correlations between forecast and actual values in excess of 0.99 (99 percent) are highly desirable and indicate that the forecast model being considered constitutes an effective tool for analysis.

In cross-section analysis, in which the important trend element in most economic data is held constant, a correlation of 99 percent between forecast and actual values is rare. When unusually difficult forecasting problems are being addressed, correlations between forecast and actual data of 90 percent or 95 percent may prove satisfactory. By contrast, in critical decision situations, forecast values may have to be estimated at very precise levels. In such instances, forecast and actual data may have to exhibit an extremely high level of correlation, 99.5 percent or 99.75 percent, to generate a high level of confidence in forecast reliability.

sample mean forecast error

Estimate of average forecast error