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 the first and second quarters 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 seasonal and seasonal subseries plots for the *Effective hours of work *series. The mean for each quarter varies between 112% and 157% with *Effective hours of work* in the third quarter being at the highest level. The lowest value was in the first quarter. However, the seasonal patterns look quite similar in almost all four quarters with the first quarter being the only exception.

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 quarter with the highest volatility in *Effective hours of work*: third quarter. The seasonal boxplots and seasonal distribution plots show a very little variation in *Effective hours of work *in the first quarter (excluding outliers). Detrended as well as the original series show that *Effective hours of work *in the third quarter being at the highest level on average, while the lowest average value was in the first quarter.

Figure 3 shows seasonal and seasonal subseries plots for the
*Value of construction work performed *series.
The means for each quarter between the lowest in the first quarter and the highest
in the fourth quarter.

Due to the positive trend in *Value of construction work performed *series the seasonal plot shows high values at the end and lower values at the beginning of the observed period. The seasonal subseries plot for *Value of construction work performed *shows a little variation in the mean values and quite similar seasonal pattern in each quarter (first quarter is an exception).

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 in Figure 4 we can identify quarter with the highest volatility in the *Value of construction work performed *series: the third quarter. The seasonal boxplots and seasonal distribution plots show very little variations in the *Value of construction work performed *series. Detrended series shows that the *Value of construction work performed *in the fourth quarter being at the highest level on average, while the lowest average value was in the first quarter.

Figure 5 shows seasonal and seasonal subseries plots for the *Number of completed apartments *series. The means for each quarter between the lowest in the first quarter and the highest in the fourth quarter.

Due to the negative trend in *Number of completed apartments *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 *Number of
completed apartments *shows a little variation in the mean values (the
fourth quarter is an exception) and quite different seasonal patterns in each quarter.

As before, the trend component was removed and then the
plots were generated again. Variations of these plots are shown in Figure 6. *p-val: 0* on these plots indicates that
the seasonal component was statistically significant in this series.

From the seasonal boxplots we can identify quarter with highest
volatility in the *Value of construction
work performed* series: the fourth quarter. The seasonal boxplots and
seasonal distribution plots show quite large variations in the *Number of completed apartments *series. Detrended
series shows that the *Number of completed
apartments *in the fourth quarter being at the highest level on average,
while the lowest average value was in the first quarter.