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Montenegro: 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 Montenegro total tourists arrival. The means for each month varies between 20 and over 480 thousand tourists with total tourists arrival in August being at the highest level on average. The lowest values were in January February, November and December. It looks like the seasonal patterns show some changes in this period. However, due to the trend component in this and other Montenegrin 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 boxplots we can identify months with highest volatility in the total tourists arrival: July and August. 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, February and December.

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 a little variations around a constant level for respective months indicating a quite stable seasonal patterns around year. In simple terms it means there is no tendency of increasing/decreasing total 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

Seasonal component for the domestic tourists arrival is quite similar to the seasonal component of the total tourists arrival. August and July are the most volatile months in terms of the domestic tourists arrival time series as shown on the seasonal boxplots.

The seasonal boxplots and seasonal distribution plots show a very little variation in the domestic tourists arrival in other months. 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 November and February. Most of the seasonal subseries plots show variation around constant levels 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 of the total tourists overnight stay series has similar patterns as the seasonal component of the total tourists arrival: most volatile months are August and July and at the same time these months are with the highest average values. 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 total tourists overnight stay in a particular month in the observed period.

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

The seasonal component of the domestic tourists overnight stay series has similar patterns as the seasonal component of the domestic tourists arrival: most volatile months are August and July and at the same time these months are with the highest average values. 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

Because 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.