Transcript Document 7171816

Forecasting with Intervention:
Tourism in Croatia
Ante Rozga,
Toni Marasović, Josip Arnerić
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
Nigths in 000
18000
16000
14000
12000
10000
8000
6000
4000
2000
date
0
Sij94
Sij96
Sij98
Sij2000
Sij2002
Sij2004
Sij2006
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Figure 2. Seasonal factors extracted by X-12-ARIMA and
TRAMO/SEATS
Final seasonal f actors - Model 1 (Tramo-Seats)
Final seasonal f actors - Model 2 (X-12-Arima)
4.9
4.2
3.5
2.8
2.1
1.4
0.7
date
0
Sij94
Sij96
Sij98
Sij2000
Sij2002
Sij2004
Sij2006
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Figure 3. Final trend with X-12-ARIMA and TRAMO/SEATS
Final trend - Model 1 (Tramo-Seats)
Final trend - Model 2 (X-12-Arima)
4800
4400
4000
3600
3200
2800
2400
2000
1600
1200
date
800
Sij94
Sij96
Sij98
Sij2000
Sij2002
Sij2004
Sij2006
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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
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%
--
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%
--
6.26% [0%, 15.0%] ad-hoc
3.59% [0%, 5.0%] ad-hoc
2.40% [0%, 5.0%] ad-hoc
--
0.15 [0, 1] ad-hoc
STATISTICS ON RESIDUALS
DESCRIPTION OF RESIDUALS
FORECAST ERROR
Forecast error over last year
OUTLIERS
Percentage of outliers
CRITERIA FOR DECOMPOSITION
Combined statistic Q (M1, M3-M11)
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Figure 4. Final seasonally adjusted seris
Final seasonally adjusted series - Model 1 (Tramo-Seats)
Final seasonally adjusted series - Model 2 (X-12-Arima)
5100
4800
4500
4200
3900
3600
3300
3000
2700
2400
2100
1800
1500
1200
900
date
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Sij94
Sij96
Sij98
Sij2000
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Sij2006
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Figure 5. Final trend
Final trend - Model 1 (Tramo-Seats)
Final trend - Model 2 (X-12-Arima)
4800
4400
4000
3600
3200
2800
2400
2000
1600
1200
date
800
Sij94
Sij96
Sij98
Sij2000
Sij2002
Sij2004
Sij2006
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Figure 6. Final irregular factors
Final irregular f actors - Model 1 (Tramo-Seats)
Final irregular f actors - Model 2 (X-12-Arima)
1.36
1.28
1.2
1.12
1.04
0.96
0.88
0.8
0.72
0.64
0.56
0.48
date
0.4
Sij94
Sij96
Sij98
Sij2000
Sij2002
Sij2004
Sij2006
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Figure 7. Forecasts by both methods
Lower conf idence limit f or Forecasts - Model 2 (X-12-Arima)
Upper conf idence limit f or Forecasts - Model 2 (X-12-Arima)
Forecast of orig. uncorr. series - Model 2 (X-12-Arima)
Lower conf idence limit f or Forecasts - Model 1 (Tramo-Seats)
Upper conf idence limit f or Forecasts - Model 1 (Tramo-Seats)
Forecast of orig. uncorr. series (with Tramo model) - Model 1 (Tramo-Seats)
36000
32000
28000
24000
20000
16000
12000
8000
4000
date
0
Sij2006
Sij2007
Sij2008
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To take advantages both from X-12-ARIMA and TRAMO/SEATS
researchers from CENSUS Bureau are developing hybrid X-13ARIMA-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.
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