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about former Yugoslav republics economies

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Real Sector Tourism

Slovenia: Seasonality in tourism 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 June and July 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 Slovenia total tourists arrival. The means for each month varies between 190 and over 550 thousand tourists with total tourists arrival in August being at the highest level on average. The lowest values were in January and November. It looks like the seasonal patterns show some changes in this period. However, due to the trend component in this and other Slovenian tourism time series, these changes in the seasonal patterns on the seasonal plot are not quite clear. Therefore we have removed the trend component and conducted the seasonality analysis on the detrended series as shown on variations of these plots in the remaining figures (Figures 2 to 7).

Seasonal and seasonal subseries plots: Total tourists arrival
Figure 1. Seasonal and seasonal subseries plots: Total tourists arrival

p-val: 0 on these plots indicates that the seasonal component was statistically significant. From the seasonal plots we can see that there are less variations in the later years than at the beginning of the observed period (dark blue lines are clustered together). The seasonal boxplots tell us that there is a little variation in the total tourists arrival, the largest was in July. The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists arrival in the other months. Detrended as well as the original series show that total tourists arrival in August and July being at the highest level on average, while the lowest average values were in January and November.

Seasonal, boxplot, subseries and distribution plots: Total tourists arrival
Figure 2. Seasonal, boxplot, subseries and distribution plots: Total tourists arrival

Most of the seasonal subseries plots show variation around some constant level for respective months. In simple terms it means there is no tendency of increasing/decreasing yoyal tourists arrival in a particular month in the observed period.

Seasonal, boxplot, subseries and distribution plots: Domestic tourists arrival
Figure 3. Seasonal, boxplot, subseries and distribution plots: Domestic tourists arrival

From the seasonal boxplots we can identify months with highest volatility in the domestic tourists arrival time series: August and July. The seasonal boxplots and seasonal distribution plots show slightly more variation in the domestic tourists arrival in comparison to variation in total and foreign tourists arrival series. Detrended series show that domestic tourists arrival in August and July being at the highest level on average, while the lowest average values were in January and November.

Most of the seasonal subseries plots show variation around some constant level for respective months. In simple terms it means there is no tendency of increasing/decreasing domestic tourists arrival in a particular month in the observed period.

Seasonal, boxplot, subseries and distribution plots: Foreign tourists arrival
Figure 4. Seasonal, boxplot, subseries and distribution plots: Foreign tourists arrival

Because the foreign tourists arrival is a major component of the total tourists arrival the comments related to seasonality patterns observed in the total tourists arrival series apply also to the foreign tourists arrival series.

Seasonal, boxplot, subseries and distribution plots: Total tourists overnight stay
Figure 5. Seasonal, boxplot, subseries and distribution plots: Total tourists overnight stay

The seasonal component in the total tourists overnight stay shows very similar pattern as the total tourists arrival series.

Seasonal, boxplot, subseries and distribution plots: Domestic tourists overnight stay
Figure 6. Seasonal, boxplot, subseries and distribution plots: Domestic tourists overnight stay

From the seasonal plots we can see that there are less variations in the later years than at the beginning of the observed period (dark blue lines are clustered together). From the seasonal boxplots we can identify months with highest volatility in the domestic tourists overnight stay time series: July and August. The seasonal boxplots and seasonal distribution plots show a very little variation in the domestic tourists overnight stay in other months, but more than total and foreign tourist overnight stay series. Detrended series show that domestic tourists overnight stay in August and July being at the highest level on average, while the lowest average values were in January and November.

Most of the seasonal subseries plots show variation around some constant level for respective months. In simple terms it means there is no tendency of increasing/decreasing domestic tourists arrival in a particular month in the observed period.

Seasonal, boxplot, subseries and distribution plots: Foreign tourists overnight stay
Figure 7. Seasonal, boxplot, subseries and distribution plots: Foreign tourists overnight stay

FBecause the foreign tourists overnight stay is a major component of the total tourists overnight stay the comments related to seasonality patterns observed in the total tourists overnight stay series apply also to the foreign tourists overnight stay series.

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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.