Removing the seasonal effect

Having estimated a common seasonal effect that describes how far each month's value is (on average) from the overall trend, we can subtract this seasonal effect to obtain deseasonalised data. This is often called seasonally adjusting the data.

Since we have a seasonal effect for every month, it is possible to deseasonalise up to both ends of a time series. This is an important advantage over smoothing out the seasonal effect with moving averages.

The deseasonalised data not only shows the trend in the series more clearly, but also shows individual months that are substantially different from the usual seasonal pattern.

Monthly temperatures in Boulder, Colorado

The time series plot below shows mean monthly temperature in Boulder Colorado and the corresponding deseasonalised data.

The seasonal effects are shown at the bottom of the diagram. Click on the December seasonal effect. All deseasonalised values for December are the actual December temperatures minus the December seasonal effect. (This is highlighted in red on the top time series plot). Note that all December temperatures are reduced by the same amount to deseasonalise them.

The peaks and troughs of the deseasonalised series clearly show 'unusual' months. In particular,

November 2000 was particularly cold (for a November) but November 1999 was a very warm November

This information is not clear from the raw data.