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Bosnia and Herzegovina: 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 Bosnia and Herzegovina total tourists arrival. The means for each month varies between 40 and 90 thousand with total tourists arrival in May being at the highest level on average. The lowest values were in January and February. It looks like the seasonal patterns show some changes in this period. However, due to the trend component in this and other Bosnia and Herzegovina 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 time series: August and July. The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists arrival in April and December. Detrended as well as the original series show that total tourists arrival in May and June being at the highest level on average, while the lowest average values were in January and February.

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: January, February, March, November and December a negative trend in the total tourists arrival is recorded. At the same in July, August and September an increasing trend in the total tourists arrival is recorded. In other words, in the later years more and more tourists arrived in summer months then 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: June, July and May. The seasonal boxplots and seasonal distribution plots show a very little variation in the domestic tourists arrival in February (excluding outliers) and November. Detrended series show that domestic tourists arrival in May and June being at the highest level on average, while the lowest average values were in January and February.

Most of the seasonal subseries plots show variation around some constant level for respective months. However, we may say that the negative trend is recorded in the June subseries plot, while a positive trend is visible in the December subseries plot. In simple terms it means more and more domestic tourists arrived in December in the later years, while at the same time less and less domestic tourists arrived in June 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

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

From the seasonal boxplots we can identify months with highest volatility in the total tourists overnight stay time series: July, August and May. The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists overnight stay in March 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 January and February.

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 July and August subseries plots (after 2013). In simple terms it means more and more total tourists overnight stayed in July and August in the later years (after 2013). As we can see in Figure 7 (seasonal subseries plots) that was mostly caused by longer overnight stay of foreign tourists.

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 June. The seasonal boxplots and seasonal distribution plots show a very little variation in the domestic tourists overnight stay in November (excluding outliers). Detrended series show that domestic tourists overnight stay in May, June 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 April, July and December subseries plots (after 2013). In simple terms it means more and more domestic tourists overnight stayed in April, July and December in the later years (after 2013).

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.