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 groups and within group patterns (e.g., do first and fourth quarter exhibit similar patterns), nature and changes of seasonality within particular season. The horizontal lines on this plot indicate the means for each quarter.

Figure 1 shows Bosnia and Herzegovina seasonal and seasonal subseries plots for quarterly GDP time series. There is a large jump in GDP in the third quarter each year. The seasonal plot also shows that in the first quarter the smallest GDP was recorded.

Levels of the curves on the seasonal plot indicate increasing trend in quarterly GDP. This trend makes a bit difficult to read and interpret nature and changes in seasonal patterns. Therefore the trend was removed and these graphs were generated again. Variations of these plots are shown in Figure 2.

First, p-val: 0 on these plots indicates that the seasonal component was statistically significant in this series. Second, now it is clear what the changes were in seasonal pattern. From the seasonal plot we can notice again that the highest GDP was recorded in the third quarter, but this time we can also notice that in the last few years level of GDP in this quarter decreased. This is even more clear on the seasonal subseries plot where we have a negative trend in GDP in this quarter, but and increasing trend in the first quarter. GDP in the second and fourth quarters stay at approximately same level in the observed period.

From the seasonal boxplot we can identify quarters with highest volatility in GDP: third and first quarters. In other two quarters there were small variation in GDP.

Seasonal distribution plot is an alternative plot to seasonal boxplot. It also shows level of variation in seasonal component by quarter.