Forecasting with Intervention: Tourism in Croatia

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Forecasting with Intervention Tourism in Croatia

• Ante Rozga,
• Toni Marasovic, Josip Arneric
• University of Split,
• Croatia

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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.

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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.

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3. Results

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

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Figure 2. Seasonal factors extracted by
X-12-ARIMA and TRAMO/SEATS
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Figure 3. Final trend with X-12-ARIMA and
TRAMO/SEATS
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Method Tramo/Seats X-12-Arima
Transformation Logarithm Logarithm
Mean Correction Yes Yes
Correction for Trading Day Effects 1 Regressor(s) 6 Regressor(s)
Correction for Easter Effect Yes (6 day(s)) Yes (6 day(s))
Correction for Outliers Autom.AO,LS,TC 6 Outlier(s) fixed Autom.AO,LS,TC 4 Outlier(s) fixed
Critical t-value 3,3 3,914
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-value 4.58 -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-value 3.77 -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 None
Corr. for Other Regr. Effects None None
Specif. of the ARIMA model (1 0 0)(0 1 0) (fixed) (2 1 0)(0 1 1) (fixed)
ARIMA Decomposition Exact --
X-11 Decomposition -- With ARIMA forecasts
X-11 Seasonal Filter -- 3x3 MA
X-11 Trend Filter -- 13-term Henderson MA
Seasonality Seasonal model used Significant
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Information on Diagnostics Model 1 (Tramo-Seats) Model 2 (X-12-Arima)
SA quality index (stand. to 10) 3.554 0, 10 ad-hoc 5.632 0, 10 ad-hoc
STATISTICS ON RESIDUALS    
Ljung-Box on residuals 32.17 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 residuals 11.94 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 outliers 3.59 0, 5.0 ad-hoc 2.40 0, 5.0 ad-hoc
CRITERIA FOR DECOMPOSITION    
Combined statistic Q (M1, M3-M11) -- 0.15 0, 1 ad-hoc
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Figure 4. Final seasonally adjusted seris
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Figure 5. Final trend
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Figure 6. Final irregular factors
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Figure 7. Forecasts by both methods
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• 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.

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• 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.

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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.