Stylized Facts

about former Yugoslav republics economies

Industrial production Real Sector

Croatia: 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 88% and 106% with industrial production index in October being at the highest level on average. The lowest values were in January. There are some similarities in the seasonal patterns in all 12 months.

Figure 1. Seasonal and seasonal subseries plots

The line graph in previous blog post shows an increasing trend in industrial production at the beginning of period and less prominent increase after 2012. However, negative trend was recorded from 2008 until 2012. Therefore the formal statistical test indicated that in the whole period 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. Croatia: 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 see that the industrial production indices are quite volatile. The seasonal boxplots and seasonal distribution plots show less variations in the industrial production indices in July (excluding outliers). Industrial production indices in October and September being at the highest level on average, while the lowest average values were in January, February and August.


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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.