1. 1 Forecasting with Intervention: Tourism in Croatia Ante Rozga, Toni Marasović, Josip Arnerić University of Split, Croatia

2. 2 1. Introduction Tourism is among the most vulnerable business activities. It could be affected by political crisis, outbreak of the desease, economic crisis and war activities. In Croatia, the war for independence in 1991 affected tourism seriously. The number of foreign tourist has fallen more than 85% in 1992, compared with 1989. But, there were another interventions: the military action “Storm” in August 1995 for deliberation of occupied Croatian teritories and NATO strike in 1999 against Serbia, connected with Kosovo crisis. Although NATO action was not conducted on Croatian teritory, the action had impact on Croatian tourism.

3. 3 2. Methods We have used several satistical methods to analyze seasonal and other variations in monthly time series. Some of them are empirically based while the others were models based methods. We compared their performance to see the difference. We concentrated mostly on three of them: 2.1. X-12-ARIMA, developed by the Census Bureau, U.S.A. It is empirically based method (“ad-hoc method”), still dominant method for seasonal adjustment throughout the world. 2.2. TRAMO/SEATS, developed in Banco de España, Madrid, by Gomes, Maravall and Caporello. This method is popular in EU. 2.3. Structural Time Series Model developed by Harvey and others, computer programe by Timberlake Consultancy Inc.

4. 4 3. Results We have analyzed nights spent by tourists from July 1993 until April 2007. Figure 1. Nights in 000

5. 5 Figure 2. Seasonal factors extracted by X-12-ARIMA and TRAMO/SEATS

6. 6 Figure 3. Final trend with X-12-ARIMA and TRAMO/SEATS

7. 7 MethodTramo/SeatsX-12-Arima TransformationLogarithm Mean CorrectionYes Correction for Trading Day Effects1 Regressor(s)6 Regressor(s) Correction for Easter EffectYes (6 day(s)) Correction for OutliersAutom.:AO,LS,TC; 6 Outlier(s) fixedAutom.:AO,LS,TC; 4 Outlier(s) fixed Critical t-value3,33,914 AO Ruj1995 t-value-6.84 [-3.300, 3.300] crit.val.-- TC Kol1995 t-value-7.09 [-3.300, 3.300] crit.val.-- TC Svi1995 t-value-5.28 [-3.300, 3.300] crit.val.-- AO Svi2002 t-value4.58 [-3.300, 3.300] crit.val.4.01 [-3.914, 3.914] crit.val. AO Svi2000 t-value-3.73 [-3.300, 3.300] crit.val.-- AO Svi1997 t-value3.77 [-3.300, 3.300] crit.val.-- LS Svi1995 t-value---5.28 [-3.914, 3.914] crit.val. LS Kol1995 t-value---5.68 [-3.914, 3.914] crit.val. LS Lis1995 t-value--7.69 [-3.914, 3.914] crit.val. Corr. for Missing Obs.None Corr. for Other Regr. EffectsNone Specif. of the ARIMA model(1 0 0)(0 1 0) (fixed)(2 1 0)(0 1 1) (fixed) ARIMA DecompositionExact-- X-11 Decomposition--With ARIMA forecasts X-11 Seasonal Filter--3x3 MA X-11 Trend Filter--13-term Henderson MA SeasonalitySeasonal model usedSignificant

8. 8 Information on DiagnosticsModel 1 (Tramo-Seats)Model 2 (X-12-Arima) SA quality index (stand. to 10)3.554 [0, 10] ad-hoc5.632 [0, 10] ad-hoc STATISTICS ON RESIDUALS Ljung-Box on residuals32.17 [0, 35.20] 5%15.02 [0, 51.20] 0.1% Box-Pierce on residuals 1.95 [0, 5.99] 5%-- Ljung-Box on squared residuals11.94 [0, 35.20] 5%-- [0, ?] 0.1% Box-Pierce on squared residuals 0.02 [0, 5.99] 5%-- DESCRIPTION OF RESIDUALS Normality 4.29 [0, 5.99] 5%-- Skewness 0.12 [-0.40, 0.40] 5%-- Kurtosis (significant) 3.80 [2.21, 3.79] 5% 4.84 [1.75, 4.25] 0.1% FORECAST ERROR Forecast error over last year-- 6.26% [0%, 15.0%] ad-hoc OUTLIERS Percentage of outliers3.59% [0%, 5.0%] ad-hoc2.40% [0%, 5.0%] ad-hoc CRITERIA FOR DECOMPOSITION Combined statistic Q (M1, M3-M11)--0.15 [0, 1] ad-hoc

9. 9 Figure 4. Final seasonally adjusted seris

10. 10 Figure 5. Final trend

11. 11 Figure 6. Final irregular factors

12. 12 Figure 7. Forecasts by both methods

13. 13 To take advantages both from X-12-ARIMA and TRAMO/SEATS researchers from CENSUS Bureau are developing hybrid X-13- ARIMA-SEATS, which would integrate the best from empirically based method and method based one.

14. 14 We have used STAMP program which uses structural time series modelling. Series = trend + seasonal + intervention + irregular All these components could be handled in several different ways. The results were satisfactory.

15. 15 Conclusion After trying several forecasting and decomposition methods for tourism in Croatia we conclude that method TRAMO/SEATS is sligtly better when it comes to handling interventions in time series.