Stylized Facts

about former Yugoslav republics economies

Industrial production Real Sector

Montenegro: Seasonality analysis of monthly industrial production 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 January 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 industrial production time series. The means for each month varies between 85% and 111% with industrial production index in December being at the highest level on average. The lowest values were in June and May. There are a lot of variations in the seasonal patterns in all 12 months. However, because of the series length this observation should be taken with caution.

Figure 1. Seasonal and seasonal subseries plots

The line graph in previous blog post shows that there is no clear trend in industrial production. It seems that the industrial production indices vary around a constant level. Therefore the formal statistical test indicated that the trend component was not statistically significant.

Variations of seasonal plots are shown in Figure 2. p-val: 0 on these plots indicates that the seasonal component was statistically significant in this series.

Figure 2. Montenegro: Seasonal, boxplot, subseries and distribution plots

From the seasonal boxplots we can identify months with highest volatility in the industrial production indices: April and March. The seasonal boxplots and seasonal distribution plots show a very little variation in the industrial production indices in September and July (excluding outliers). Industrial production indices in March and November being at the highest level on average, while the lowest average values were in June and May.


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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.