Stylized Facts

about former Yugoslav republics economies

Real Sector Transportation

Seasonality analysis of Serbian quarterly transportation 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 Volume of services in road passenger transport series. The mean for each quarter varies between 1050 and 1170 million passenger km with Volume of services in road passenger transport 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.

Figure 1. Seasonal and seasonal subseries plots:
Value of services in road passenger transport

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 Volume of services in road passenger transport: the second quarter. The seasonal boxplots and seasonal distribution plots show less variations in Volume of services in road passenger transport in the first quarter (excluding outlier). The Volume of services in road passenger transport seriesin 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:
Value of services in road passenger transport

Figure 3 shows seasonal and seasonal subseries plots for the Volume of services in road freight transport series.

Figure 3. Seasonal and seasonal subseries plots:
Value of services in road freight transport

Due to the positive trend in Volume of services in road freight transport 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 Volume of services in road freight transport shows a little variation in the mean values and quite similar seasonal pattern in each quarter.

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 services in road freight transport

From the seasonal boxplots in Figure 4 we can identify quarter with the highest volatility in the Volume of services in road freight transport series: the second quarter and the third quarter with the lowest volatility. Detrended series shows that the Volume of services in road freight transport in the second 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.