Seasonal adjustment MA


The Seasonal adjustment MA  (SA) analysis removes the seasonal pattern from a series using moving averages. The algorithm used is not as advanced as in Seasonal adjustment Census X-13, but is much faster and easier to use and works well in many cases. The method works by calculating a seasonal factor for each period and then adjusting all the values in the series with these factors. The analysis will produce the adjusted series as a time series and the seasonal factors as a category series.


The trend is removed by subtracting or dividing the series with a long moving average. The number of observations in the moving average is the number of observations in a year based on the frequency. Monthly factors, however, will be used for all series with higher frequency than a month.

Seasonal factors are found by calculating the mean for each period within the estimation range. The factors are then normalized so that the sum is 0, for the additive method, or 1, for the multiplicative method.

The adjusted time series is then created by subtracting or dividing by the factors.




It removes the seasonal component by subtracting the average deviation from the mean for the period. This method works best if the series is relatively constant over time.


It removes the seasonal component by dividing by the average factor compared to the mean for the period. It works better if the seasonal factor is proportional to the level of the series, which is often the case when the series shows an exponential pattern.


Multiplicative method

This chart shows the US Industrial Production Index series both seasonally adjusted and unadjusted. We used multiplicative method do adjust the series. In “Seasonal weights” category chart the weights per month can be viewed.