Stylized Facts

about former Yugoslav republics economies

Real Sector Wages

Seasonality analysis of Serbian monthly wages 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 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 average gross wages time series. The means for each month varies between 47000 and 58000 dinars with average gross wages in December being at the highest level. The lowest values were in January. However, the seasonal patterns look quite similar in almost all 12 months.

Figure 1. Seasonal and seasonal subseries plots: Average gross wages

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 the average gross wages: January and March (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show a very little variation in the average gross wages from September to November. Detrended as well as the original series show that the average gross wages in December being at the highest level on average, while the lowest average value was in January.

Figure 2. Seasonal, boxplot, subseries and distribution plots: Average gross wages

Figure 3 shows seasonal and seasonal subseries plots for the average net wages time series. Similarly to the graphs in Figure 1 the means for each month varies lowest in January and highest in December.

Figure 3. Seasonal and seasonal subseries plots: Average net wages

The seasonal and seasonal subseries plots for the average net wages are similar to the same graphs for the average gross wages.

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: Average net wages

We can make similar comments as we made with these plots for the average gross wages series. From the seasonal boxplots we can identify months with highest volatility in the average gross wages: January, March and April (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show a very little variation in the average net wages from September to November and again, ignoring a few outliers. Detrended as well as the original series show that the average net wages in December being at the highest level on average, while the lowest average value was in January.

Figure 5 shows seasonal and seasonal subseries plots for the unit labor costs in industry time series. The highest unit labor cost was in January and the lowest in September and October.

Figure 5. Seasonal and seasonal subseries plots: Unit labor costs in industry

Because the trend component was not statistically significant it was not removed from this series. 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: Unit labor costs in industry

From the seasonal boxplots we can identify months with highest volatility in the unit labor costs in industry: February and July (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show some variation in the unit labor costs in industry: below average from September to December and above average in the first quarter. These graphs show that the unit labor costs in industry in January being at the highest level on average, while the lowest average value was in September and October.

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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.