In exponential smoothing, R-squared is used to indicate how much better or worse the forecast is than what baseline?

• A. The slope of the trend
• B. The variance of residuals
• C. The correlation between actual and forecast
• D. Uses R² to tell us how much better, or worse, the forecast is than a horizontal line

Answer: (D)

The main idea is how well the forecast performs compared with a simple, flat baseline: predicting every period as the historical average, which is a horizontal line. R-squared measures how much of the observed variation in the data is explained by the forecast beyond this baseline. It’s computed as 1 minus the ratio of the forecast error sum of squares to the total sum of squares around the baseline mean. If the exponential smoothing forecast reduces errors substantially versus always predicting the mean, R-squared moves toward 1. If it doesn’t improve on the mean forecast, R-squared is near 0 or can be negative if the forecast is worse.

So, R-squared in this context tells you how much better or worse the forecast is compared with using a horizontal line at the average.