When using moving averages to analyze seasonal variation, the seasonal component is calculated as which of the following?

• A. Actual - moving avg
• B. Moving average - Actual
• C. Actual + moving average
• D. Moving average / Actual

Answer: (A)

When you use moving averages to study seasonal variation, you first smooth the data to estimate the underlying trend. In an additive setup, the observed value equals the trend plus the seasonal effect plus irregular noise. The moving average provides that trend estimate by removing the regular seasonal swings. To isolate the seasonal component, you subtract the trend estimate from the actual observation. This gives you the seasonal plus irregular portion; by averaging across periods of the same season you can extract the pure seasonal pattern. So the seasonal component is Actual minus the Moving Average. The alternative forms would be used in different modeling assumptions (for example, divide when using a multiplicative model), but for additive decomposition subtraction is the correct approach.