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Seasonality
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Many time series display seasonality, or periodic fluctuations. For example, retail sales tend to peak for the Christmas season and then decline after the holidays. So time series of retail sales will typically show increasing sales from September through December and declining sales in January and February.
Seasonality is quite common in economic time series. It is less common in engineering and scientific data, though a notable scientific data set showing seasonality is the concentration of atmospheric carbon dioxide: it is at a minimum in September and October, and steadily increases from then until June and then begins declining again until September.
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Encyclopedia
Many time series display seasonality, or periodic fluctuations. For example, retail sales tend to peak for the Christmas season and then decline after the holidays. So time series of retail sales will typically show increasing sales from September through December and declining sales in January and February.
Seasonality is quite common in economic time series. It is less common in engineering and scientific data, though a notable scientific data set showing seasonality is the concentration of atmospheric carbon dioxide: it is at a minimum in September and October, and steadily increases from then until June and then begins declining again until September. Another scientific example are the famous Milankovitch cycles.
If seasonality is present, it can be incorporated into a time series model.
Detecting seasonality
In this section, techniques for detecting seasonality are discussed. The following graphical techniques can be used to detect seasonality:
- A run sequence plot will often show seasonality
- A seasonal subseries plot is a specialized technique for showing seasonality
- Multiple box plots can be used as an alternative to the seasonal subseries plot to detect seasonality
- The autocorrelation plot can help identify seasonality
- Seasonal Index measures how much the average for a particular period tends to be above (or below) the expected value
The run sequence plot is a recommended first step for analyzing any time series. Although seasonality can sometimes be indicated with this plot, seasonality is shown more clearly by the seasonal subseries plot or the box plot. The seasonal subseries plot does an excellent job of showing both the seasonal differences (between group patterns) and also the within-group patterns. The box plot shows the seasonal difference (between group patterns) quite well, but it does not show within group patterns. However, for large data sets, the box plot is usually easier to read than the seasonal subseries plot.
Both the seasonal subseries plot and the box plot assume that the seasonal periods are known. In most cases, the analyst will in fact know this. For example, for monthly data, the period is 12 since there are 12 months in a year. However, if the period is not known, the autocorrelation plot can help. If there is significant seasonality, the autocorrelation plot should show spikes at lags equal to the period. For example, for monthly data, if there is a seasonality effect, we would expect to see significant peaks at lag 12, 24, 36, and so on (although the intensity may decrease the further out we go).
Seasonal adjustment
See also
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