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 June 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 the employment time series. The means for each month vary between 1920 and 1975 thousands with employment in July being at the highest level. The lowest values were in January. However, the seasonal patterns look quite similar in almost 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.

From the seasonal boxplots we can identify months with highest volatility in employment: February and March. The seasonal boxplots and seasonal distribution plots show a very little variation in employment in August, September and November. Detrended as well as the original series show that employment in July being at the highest level on average, while the lowest average value was in January.

Figure 3 shows seasonal and seasonal subseries plots for the number of unemployed persons time series. The means for each month vary between the lowest in August and the highest in March.

Due to the negative trend in unemployment time series the seasonal plot shows high values at the beginning and lower values at the end of the observed period. The seasonal subseries plots for unemployment shows a little variation in the mean values and quite similar seasonal pattern in each month.

As before, the trend component was removed and then the plots were generated again. Variations of these plots are shown in Figure 4. p-val: 0 on these plots indicates that the seasonal component was statistically significant in this series.

From the seasonal boxplots we can identify months with highest volatility in the unemployment series: February and March (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show quite large variations in the unemployment series. Detrended series shows that the unemployment in February and March being at the highest level on average, while the lowest average value was in November.