Classical Seasonal Decomposition (Census Method 1) - Computations

Computationally, the Seasonal Decomposition (Census I) procedure of the Time Series module closely follows the standard formulas, as shown in Makridakis, Wheelwright, and McGee (1983), and Makridakis and Wheelwright (1989).

Element Name Description
Moving average First a moving average is computed for the series, with the moving average window width equal to the length of one season. If the length of the season is even, then you can use either equal for the moving average, unequal weights, where the first and last observation in the moving average window are averaged (select the Centered moving averages (for even Seasonal lag only) check box on the Advanced tab of the Ratios-To-Moving averages Classical Decomposition (Census Method I) dialog).
Ratios or differences In the moving average series, all seasonal (within-season) variability will be eliminated; thus, the differences (in additive models) or ratios (in multiplicative models) of the observed and smoothed series will isolate the seasonal component (plus irregular component). Specifically, the moving average is subtracted from the observed series (for additive models) or the observed series is divided by the moving average values (for multiplicative models).
Seasonal components The seasonal component is then computed as the average (for additive models) or medial average divided by the overall mean of the medial averages multiplied by 100 (for multiplicative models) for each point in the season. (The medial average of a set of values is the mean after the smallest and largest values are excluded). The resulting values represent the (average) seasonal component of the series.
Seasonally adjusted series The original series can be adjusted by subtracting from it (additive models) or dividing it by (multiplicative models) the seasonal component. The resulting series is the seasonally adjusted series (i.e., the seasonal component will be removed).
Trend-cycle component Remember that the cyclical component is different from the seasonal component in that it is usually longer than one season, and different cycles can be of different lengths. The combined trend and cyclical component can be approximated by applying to the seasonally adjusted series a 5 point (centered) weighed moving average smoothing transformation with the weights of 1, 2, 3, 2, 1.
Random or irregular component Finally, the random or irregular (error) component can be isolated by subtracting from the seasonally adjusted series (additive models) or dividing the adjusted series by (multiplicative models) the trend-cycle component.