There are a few time series graphs we can use to identify underlying seasonal pattern. These are seasonal and seasonal subseries plots, with some variations in their appearance.

A seasonal plot is similar to a time plot except that the data are plotted against the individual “seasons” in which the data were observed. A seasonal plot allows the underlying seasonal pattern to be seen more clearly and to identify years in which the pattern changes.

A seasonal subseries plot is another graphical tool for detecting seasonality in a time series. This plot allows you to detect both between group and within group patterns (e.g., do January and December exhibit similar patterns), nature and changes of seasonality within particular season. The horizontal lines on this plot indicate the means for each month.

Figure 1 shows seasonal and seasonal subseries plots for monthly industrial production time series. The means for each month varies between 72% and 99% with industrial production index in November being at the highest level on average. The lowest values were in January and February. There are a lot of variations in the seasonal patterns in all 12 months.

Because of the trend in time series it might be difficult to spot the changes in the seasonal pattern. Therefore the trend component was removed and then the plots were generated again. Variations of these plots are shown in Figure 2. p-val: 0 on these plots indicates that the seasonal component was statistically significant in this series.

We can see from the seasonal plots that variation in seasonal component decreased in the later years (dark blue lines are clustered together). From the seasonal boxplots we can identify months with highest volatility in the industrial production indices: June and November. The seasonal boxplots and seasonal distribution plots show a very little variation in the industrial production indices in January and March. Detrended as well as the original series show that industrial production indices in November being at the highest level on average, while the lowest average values were in January and February.