Which measure shows how correlated the historical actual values are to the forecasts?

The measure that best indicates how correlated the historical actual values are to the forecasts is the adjusted R-squared. This metric provides insight into the proportion of the variance in the dependent variable that can be predicted from the independent variables in a regression model. While the other measures can assess the magnitude of errors in forecasts, adjusted R-squared specifically addresses the relationship between the actual values and the forecasts by evaluating how closely the predictions align with historical data.

Mean absolute error, root mean square errors, and mean percentage error are all focused on quantifying the accuracy of the forecasts by measuring the size of errors without directly conveying the correlation aspect. Therefore, while these metrics offer valuable information about forecast performance, they do not measure the strength or direction of the relationship between the actual values and the forecasts as adjusted R-squared does.