R² in exponential smoothing is used to compare forecast performance against what baseline?

R² in exponential smoothing is used to compare forecast performance against what baseline?

• A. A moving average
• B. A horizontal line
• C. The previous forecast
• D. A trend line

Answer: (B)

R^2 in this context measures how much of the variability in the actual data is explained by the forecast compared with a simple constant forecast at the data’s average. That constant forecast corresponds to a horizontal line equal to the mean of the observed values. The idea is to see if your exponential-smoothing forecast reduces errors beyond just predicting the average every period. Mathematically, you compare the forecast errors to the total variability around the mean: SS_res = sum of (actual minus forecast)^2, SS_tot = sum of (actual minus mean)^2, and R^2 = 1 − SS_res/SS_tot. If the forecast beats the mean, R^2 is positive; if it’s no better than the mean, R^2 is near zero; if it’s worse, R^2 can be negative. So the baseline for R^2 here is a horizontal line at the mean, not a moving average, the previous forecast, or a trend line.

R^2 in this context measures how much of the variability in the actual data is explained by the forecast compared with a simple constant forecast at the data’s average. That constant forecast corresponds to a horizontal line equal to the mean of the observed values. The idea is to see if your exponential-smoothing forecast reduces errors beyond just predicting the average every period.

Mathematically, you compare the forecast errors to the total variability around the mean: SS_res = sum of (actual minus forecast)^2, SS_tot = sum of (actual minus mean)^2, and R^2 = 1 − SS_res/SS_tot. If the forecast beats the mean, R^2 is positive; if it’s no better than the mean, R^2 is near zero; if it’s worse, R^2 can be negative.

So the baseline for R^2 here is a horizontal line at the mean, not a moving average, the previous forecast, or a trend line.