ࡱ> wyv5@jbjbj22 .(XXj ....J,f$Rn!aaa a&a--v ӄ.-T60f-nn-6Tn-X0|dQ ..THE ANALYSIS OF SEASONAL VARIATIONS IN VITAL STATISTICS IN CROATIA: TWO DIFFERENT APPROACHES Ante Rozga, University of Split }eljko Banovi, 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.  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.  Figure 3.2. Monthly data for deaths in Croatia from January 1996. until January 2006.  Figure 3.3. Monthly data for marriages in Croatia from January 1996. until January 2006.  3.4. Figure 3.4. Monthly data for divorces in Croatia from January 1996 until January 2006.  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 Espaa. 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 indexX-12-ARIMATRAMO/SEATSLive births Deaths Marriages Divorces3.609 4.041 3.997 6.6701.943 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. 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. 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