THE ANALYSIS OF SEASONAL VARIATIONS IN VITAL
STATISTICS IN CROATIA: TWO DIFFERENT APPROACHES
Ante Rozga, University of Split
Željko Banović, T-Com
1. INTRODUCTION
We have analyzed the following vital statistics in Croatia: live births, deaths, marriages
and divorces. Seasonal and other variations were extracted from monthly time series. We
have also made forecasts for the nearest future. It would be interested because Croatian
population has been decreasing for several years and also number of marriages has
dramatically fallen, due to various reasons.
Two different methods for seasonal adjustment were employed: X-12-ARIMA which is
empirically based (“ad hoc method”) and TRAMO/SEATS which is model based
method. We investigated the results and statistical diagnostics related to both methods.
2. THE ANALYSIS OF THE ANNUAL HISTORICAL DATA
Since thirty years ago live births has been decreasing, but still outnumbering the number
of deaths. The number of deaths surpassed live birth at the beginning of the war for
independence, due to various reasons. Since 1991 there have been only two years with
the positive natural increase.
We can see annual changes in births and deaths from the following graph:
Figure 2.1. Deaths and births in Croatia from 1970 until 2005.
Also, we could compare number of marriages with the number of divorces:
Figure 2.2. Marriages and divorces in Croatia from 1970 until 2005.
Marriages
40000
Divorces
Number
30000
20000
10000
0
2004
2002
2000
1998
1996
1994
1992
1990
1988
1986
1984
1982
1980
1978
1976
1974
1972
1970
The number of divorces per 100 marriages has increased from 14.29 in the year 1970 to
17.79 in 2005, which is not very significant change.
3. THE ANALYSIS OF MONTHLY HISTORIC DATA:
From monthly data we could see seasonal variations in vital statistics time series.
Figure 3.1. Monthly data for live births from January 1996 until January 2006.
Liv e births
6000
5700
5400
5100
4800
4500
4200
3900
3600
3300
3000
2700
date
2400
Sij96
Sij97
Sij98
Sij99
Sij2000
Sij2001
Sij2002
Sij2003
Sij2004
Sij2005
Figure 3.2. Monthly data for deaths in Croatia from January 1996. until January
2006.
Sij2006
Deaths
6000
5750
5500
5250
5000
4750
4500
4250
4000
3750
date
3500
Sij96
Sij97
Sij98
Sij99
Sij2000
Sij2001
Sij2002
Sij2003
Sij2004
Figure 3.3. Monthly data for marriages in Croatia from January 1996. until
January 2006.
Sij2005
Sij2006
Marriages
4000
3600
3200
2800
2400
2000
1600
1200
800
date
400
Sij96
Sij97
Sij98
Sij99
Sij2000
Sij2001
Sij2002
Sij2003
Sij2004
Sij2005
3.4. Figure 3.4. Monthly data for divorces in Croatia from January 1996 until
January 2006.
Sij2006
Div orces
650
600
550
500
450
400
350
300
250
200
150
date
100
Sij96
Sij97
Sij98
Sij99
Sij2000
Sij2001
Sij2002
Sij2003
Sij2004
Sij2005
4. QUALITY OF SEASONAL ADJUSTMENT FOR VITAL STATISTICS IN
CROATIA USING TWO DIFFERENT METHODS.
Two methods are dominating seasonal adjustment in the world: X-12-ARIMA by
CENSUS Bureau and TRAMO/SEATS method from Banco de España.
The first one is empirically based but the second is model based apparoach.
The overall quality measure (Seasonal adjustment quality index) has been established to
compare different methods. Results could be seen from the following table:
Table 3.1. Seasonal adjustment quality index:
SA quality index
Live births
Deaths
Marriages
Divorces
X-12-ARIMA
3.609
4.041
3.997
6.670
TRAMO/SEATS
1.943
2.043
1.618
2.787
Series Divorces was difficult to analyze with poor seasonal adjustment quality measures
as well as other indicators.
As we could see from table 3.1 seasonal adjustment was better using method
TRAMO/SEATS for all series.
Sij2006
Series Marriages was statistically significant influenced by Easter. It is due to fact that
there were very few marriages in the period of 40 days preceding Easter.
5. FORECASTING VITAL STATISTICS IN CROATIA
6. CONCLUSION REMARKS