Stylized Facts

about former Yugoslav republics economies

Industrial production Real Sector

Slovenia: 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 80% and 100% with industrial production index in March being at the highest level on average. The lowest value was in August. There are some variations in the seasonal patterns in all 12 months.

Figure 1. Seasonal and seasonal subseries plots

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.

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

We can see from the seasonal plots that variation in seasonal component decreased in the later years (dark blue lines are clustered together). From the seasonal boxplots we can identify months with highest volatility in the industrial production indices: April and June (excluding outliers). The seasonal boxplots and seasonal distribution plots show a very little variation in the industrial production indices in August and January. Detrended as well as the original series show that industrial production indices in March being at the highest level on average, while the lowest average values were in August and December.

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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.