Stylized Facts

about former Yugoslav republics economies

Construction Real Sector

Seasonality analysis of Serbian quarterly construction time series

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.

Figure 1. Seasonal and seasonal subseries plots: Effective hours of work

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 2. Seasonal, boxplot, subseries and distribution plots: Effective hours of work

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.

Figure 3. Seasonal and seasonal subseries plots: Value of construction work performed

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.

Figure 4. Seasonal, boxplot, subseries and distribution plots:
Value of construction work performed

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.

Figure 5. Seasonal and seasonal subseries plots: Number of completed apartments

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.

Figure 6. Seasonal, boxplot, subseries and distribution plots:
Number of completed apartments

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.

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Zlatko Kovacic
Director of Wellington based My Statistical Consultant Ltd company. Retired Associate Professor in Statistics. Has a PhD in Statistics and over 35 years experience as a university professor, international researcher and government consultant.