Stylized Facts

about former Yugoslav republics economies

GDP Real Sector

Seasonality analysis of Croatia quarterly GDP 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 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.

Figure 1 shows Croatia seasonal and seasonal subseries plots for quarterly GDP time series. There is a jump in GDP in the third quarter each year. The seasonal plot also shows that in the first quarter the smallest GDP was recorded.

GDO Croatia - Seasonality analysis
Figure 1. Seasonal and seasonal subseries plots: GDP (Croatia)

Levels of the curves on the seasonal plot indicate increasing trend in quarterly GDP. The line graph in previous blog post also shows an increasing trend at the beginning of period and less prominent increase after 2008. However, the formal statistical test indicated that in the whole period trend component was not statistically significant. In Figure 2 a few variations of the seasonal plots are shown.

GDP Croatia - Seasonality analysis
Figure 2. Seasonal, boxplot, subseries and distribution plots: GDP (Croatia)

First, p-val: 0 on these plots indicates that the seasonal component was statistically significant in this series. Second, now it is clear what the changes were in seasonal pattern. From the seasonal plot we can notice again that the highest GDP was recorded in the third quarter, but this time we can also notice that in the latest years (after 2008) level of GDP in each quarter increased. This is even clearer on the seasonal subseries plot where we have an upward trend in GDP in each quarter. Third, GDP in the second and fourth quarters stay at approximately same level in the observed period.

From the seasonal boxplot and seasonal distribution plot we can identify quarters with highest volatility in GDP. It seems that the volatility of GDP was at the same level in all four quarters.


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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.