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Macedonia: 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 Macedonia total tourists arrival. The means for each month varies between 30 and over 115 thousand tourists with total tourists arrival in August being at the highest level on average. The lowest values were in February, December and January. It looks like the seasonal patterns show some changes in this period. However, due to the trend component in this and other Macedonian 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). From the seasonal boxplots we can identify months with highest volatility in the total tourists arrival time series: July and September.

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

The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists arrival in the remaining months (excluding outliers). 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 February, January 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 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

Because the domestic 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 domestic tourists arrival series.

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 September. The seasonal boxplots and seasonal distribution plots show a very large variations in the foreign tourists arrival in all months. The smaller variations were recorded in April and October. 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.

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 foreign tourists arrival is recorded. At the same time in July, August and September an increasing trend in the foreign tourists arrival is recorded. In other words, in the later years more and more foreign tourists arrived in summer months then in the same months at the beginning of the observed period.

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 and August. The seasonal boxplots and seasonal distribution plots show a very little variation in the total tourists overnight stay in all the other months. Detrended series show that total tourists overnight stay in August and July 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 July and August subseries plots. In simple terms it means more and more total tourists overnight stayed in July and 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

Because the domestic 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 domestic tourists overnight stay series.

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 September. The seasonal boxplots and seasonal distribution plots show a very little variation in the foreign tourists overnight stay in January, March and October (excluding outliers). Detrended series show that foreign tourists overnight stay in August and July being at the highest level on average, while the lowest average values were in January and December.

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 January, February, March and December subseries plot, while a positive trend is recorded in the June, July, August and September subseries plots. In simple terms it means more and more foreign tourists overnight stayed in June, July, August and September in the later years.

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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.