Stylized Facts

about former Yugoslav republics economies

Catering
Catering Real Sector

Seasonality analysis of Serbian catering 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 monthly catering time series in current prices. The means for each month varies between 60% and 75% with catering index in May and June being at the highest on average. The lowest values were in February and January. However, the seasonal patterns look quite similar in almost all 12 months.

Serbian catering series - Seasonality analysis
Figure 1. Seasonal and seasonal subseries plots: Catering series in current prices

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.

We can see from the seasonal plots that variation in seasonal component decreases in the later years. From the seasonal boxplots we can identify months with highest volatility in the catering indices: January and April (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show a very little variation in the catering indices from June to September. Detrended as well as the original series show that catering indices in May and June being at the highest level on average, while the lowest average values were in February and January.

Serbian catering series - Seasonality analysis
Figure 2. Seasonal, boxplot, subseries and distribution plots: Catering series in current prices

Figure 2 shows seasonal and seasonal subseries plots for monthly catering time series in constant prices. Similarly to the graphs in Figure 1 the means for each month varies between 80% and 100% with catering indices in May and June being at the highest on average, while the lowest values were in February and January. We can also see quite a variation in the seasonal patterns.

Serbian catering series - Seasonality analysis
Figure 3. Seasonal and seasonal subseries plots: Catering series in constant prices

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.

Serbian catering series - Seasonality analysis
Figure 4. Seasonal, boxplot, subseries and distribution plots: Catering series in constant prices

We can make similar comments as we made with these plots for series in current prices. Variation in seasonal component decreases in the later years and January and April were months with highest volatility (ignoring a few outliers). The seasonal boxplots and seasonal distribution plots show a very little variation in the catering indices from June to September. Detrended as well as the original series show that catering indices in constant prices in May and June being at the highest level on average, while the lowest average values were in February and January.

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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.