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.
Tourist arrivals in Fiji
The time series plot below shows the numbers of tourists arriving in Fiji each month between 1991 and 1999 and the corresponding deseasonalised data.
The seasonal effects are shown at the bottom of the diagram. Click on the February seasonal effect. All deseasonalised values for February are the actual February tourist numbers minus the February seasonal effect. (This is highlighted in red on the top time series plot). Note that all February tourist numbers are reduced by the same amount to deseasonalise them.
The deseasonalised data clearly show the increasing trend in the data. The peaks and troughs also show 'unusual' months. In particular,
Tourist numbers peaked more in the winters of 1998 and 1999 (May to August) than in previous winters. (After deseasonalising, there are still peaks in these winters.)
This information is not clear from the raw data.