Stylized Facts

about former Yugoslav republics economies

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GDP Real Sector

Quarterly GDP: Comparison of seasonal patterns

In this post a comparison between seasonal patterns of GDP for six countries of the former Yugoslavia is given.

As discussed before 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. All these various plots will be used to illustrate differences or similarities in seasonal patterns of GDP for these countries.

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.

Because of the trends in each GDP series (except in case of Croatia) all the quarterly GDP series were detrended.

Seasonal plots
Figure 1. Seasonal plots

From the seasonal boxplot we can identify quarters with highest volatility in GDP. Both seasonal plots and seasonal boxplots show that GDP of Bosnia and Herzegovina and Slovenia are least volatile. The most volatile GDP time series are for Croatia and Montenegro.

Seasonal boxplots
Figure 2. Seasonal boxplots

Comparing how the median value on the seasonal boxplots are changing from quarter to quarter we can identify three groups of countries. The first include Bosnia and Herzegovina and Croatia where the highest GDP is achieved in the third quarter. The second group consists of Slovenia only with highest GDP recorded in the second quarter. Finally, the third group consists of Macedonia, Montenegro and Serbia where we have an increasing trend from the first to the fourth quarter.

A seasonal subseries plot is another graphical tool for detecting seasonality in a time series. This plot allows you to detect both between groups and within group patterns (e.g., do first and fourth quarter exhibit similar patterns), nature and changes of seasonality within particular season. The horizontal lines on this plot indicate the means for each quarter.

Seasonal subseries
Figure 3. Seasonal subseries

Most of the seasonal subseries plots show variation around some constant level for respective quarters. In simple terms it means there is no tendency of increasing/decreasing GDP in a particular quarter in the observed period. Perhaps the only exception is the Macedonia GDP in the fourth quarter where a decreasing trend could be observed.

Seasonal distribution plot is an alternative plot to seasonal boxplot. It also shows level of variation in seasonal component by quarter.

Seasonal distributions (medians and confidence intervals)
Figure 4. Seasonal distributions (medians and confidence intervals)

Finally, seasonal density plot gives similar information as seasonal distribution plot. It shows the median value and the density around it using different shades of blue colour.

Seasonal density
Figure 5. Seasonal density


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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.