Stylized Facts

about former Yugoslav republics economies

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Real Sector Tourism

Serbia: 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 Serbia total tourists arrival. The means for each month varies between 130 and over 255 thousand tourists with total tourists arrival in May being at the highest level on average. The lowest values were in February and January. It looks like the seasonal patterns show some changes in this period. However, due to the trend component in this and other Serbian 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. We can see from the seasonal plots that variation in seasonal component decreases in the later years (dark blue lines are clustered together). From the seasonal boxplots we can identify months with highest volatility in the total tourists arrival: August and October. The seasonal boxplots and seasonal distribution plots show some variations in the total tourists arrival in the other months. Detrended as well as the original series show that total tourists arrival in May, August and October being at the highest level on average, while the lowest average values were in February and January.

While the tourism time series in other former Yugoslavia republics show a single peak usually in summer months (most often in August), Serbian tourism series have a few peaks (the highest in May, and then followed by peak in August and October).

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

From the seasonal subseries plots the changing nature of the seasonal component is clearly visible. In the observed period in the following months: July and August a positive trend in the total tourists arrival is recorded, while in the other months most of the values vary around constant levels. In other words, in the later years more and more tourists arrived in July and August than at the beginning of 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 October. The seasonal boxplots and seasonal distribution plots show variations in the domestic tourists arrival in other months. Detrended series show that domestic tourists arrival in May and October being at the highest level on average, while the lowest average values were in January and November.

Most of the seasonal subseries plots show variations around constant levels for respective months. However, we may say that the negative trend is recorded in the October subseries plot, while a positive trend is visible in the August subseries plot. In simple terms it means more and more domestic tourists arrived in August in the later years, while at the same time less and less domestic tourists arrived in October than at the beginning of the observed period.

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

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 foreign tourists arrival time series: August and November. The seasonal boxplots and seasonal distribution plots show quite a few variations in the foreign tourists arrival. Detrended series show that foreign tourists arrival in August and July being at the highest level on average, while the lowest average values were in January and February.

The seasonal subseries plots show variations in seasonal patterns for each month in the observed period. However, we may say that the positive trend is recorded in July and August subseries plots. In simple terms it means more and more foreign tourists arrived in July and August in the later years.

Seasonal, boxplot, subseries and distribution plots: Total tourists overnight stay
Figure 5. Seasonal, boxplot, subseries and distribution plots: Total 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 total tourists overnight stay time series: July and August. The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists overnight stay in March, April, November and December. Detrended series show that total tourists overnight stay in July and August being at the highest level on average, while the lowest average values were in November and December.

Most of the seasonal subseries plots show variation around some constant level for respective months. However, we may say that the positive trend is recorded in the August subseries plot. In simple terms it means more and more total tourists overnight stayed in August in the later years.

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: August, January and February. The seasonal boxplots and seasonal distribution plots show a very little variation in the domestic tourists overnight stay in other months. Detrended series show that domestic tourists overnight stay in July and August being at the highest level on average, while the lowest average values were in November and December.

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 overnight stay 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

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 foreign tourists overnight stay time series: July and August. The seasonal boxplots and seasonal distribution plots show a very little variation in the foreign tourists overnight stay in other months. Detrended series show that foreign tourists overnight stay in July and August being at the highest level on average, while the lowest average values were in January, February, November and December. 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 foreign tourists overnight stay in a particular month in the observed period.

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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.