Qual Quant (2011) 45:91–102DOI 10.1007/s11135-010-9338-4

Intervention analysis of SARS on Japanese tourismdemand for Taiwan

Jennifer C. H. Min · Christine Lim · Hsien-Hung Kung

Published online: 10 June 2010© Springer Science+Business Media B.V. 2010

Abstract Japan was Asia’s leading generator of international tourism in the 1980s and1990s. Japanese tourists make up over 30% of all international tourists to Taiwan and theyhave been the highest ranking tourist source market since the early stages of the island’s tour-ism development in the 1970s. However, the Severe Acute Respiratory Syndrome (SARS)outbreak in 2003, the most catastrophic disaster in the past 100 years in Taiwan, had a hugeimpact on Japanese inbound tourism to the island. The purpose of this study is to evaluatehow Japanese inbound arrivals have been affected by the SARS outbreak. A SARIMA withintervention model is used to assess the impact of the epidemic on inbound tourism fromJapan to Taiwan in the aftermath of the SARS outbreak. The empirical results indicatedthat inbound tourism from Japan was devastated by the crisis, particularly during the first5 months after the SARS outbreak. This study provides some helpful insight for the tourismindustry to respond to the impact of exogenous shock.

Keywords International tourism · Tourists · Outbreak · Impact · Intervention model

J. C. H. Min (B)International Business Department, Ming Chuan University, P.O. Box 12-12 Neihu,11499 Taipei, Taiwan, ROCe-mail: jennifer_min.tw@yahoo.com.tw

C. LimDepartment of Tourism and Hospitality Management, University of Waikato, Hamilton, New Zealand

H.-H. KungInstitute of China and Asia-Pacific Studies, National Sun Yat-Sen University, Kaohsiung, Taiwan, ROC

H.-H. KungDepartment of Marketing and Distribution Management, Hsing Wu College, Taipei, Taiwan, ROC

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1 Introduction

International tourism in 2006 continued to experience robust growth for a third straight year,with an increase of 5.4% in total visitor arrivals worldwide over the previous year to 846million. For many destinations, tourist spending on accommodation, food and drink, localtransportation, entertainment, shopping, etc, contributes a sizable proportion to their nationalincome, creating much needed employment and other opportunities for development. Tourismhas also played a significant role in enhancing Taiwan’s international exposure. In 2006, a totalof 3.5 million international travelers visited the country which is an increase of 4.19% from theprevious year. In view of this trend, a policy document entitled “Challenge 2008: Plan for Mul-tiplying Tourism”, was issued by the Executive Yuan to promote Taiwan’s tourism industry.

Japanese tourists make up over 30% of all international tourists to Taiwan and they havebeen the highest ranking tourist source since the early stages of the island’s tourism devel-opment in the 1970s. The three major factors which have contributed to the movement ofJapanese tourists to Taiwan include geographical proximity, historical and cultural ties (Lin1990). Geographically, Taiwan is the second closest democratic nation (after Korea) to Japan.The subtropical climate also attracts Japanese visitors all year round to engage in outdooractivities, such as golf, fishing, cycling, and mountain climbing. Historically, Taiwan was acolony of Japan from 1895 to 1945, prior to the Kuomintang (KMT) Party’s flight to Taiwan(from China) and its establishment of an independent government. Chiang Kai-shek, the firstchairman of the KMT, also pardoned Japanese war criminals after World War II withoutdemanding compensation. Understandably, the Chiang Kai-shek Memorial Hall is a populartourist attraction for Japanese tourists. With respect to shared culture, the written charactersof the Chinese and Japanese languages were developed from a common source in China’sTang Dynasty (sixth century A.D.) and during the half century of colonization, the cultureof Taiwan was greatly influenced by Japanese culture.

Notwithstanding the higher living costs in Taiwan, economic slowdown in Japan since themid-1990s, and the 1997 Asian financial crisis, Taiwan has remained a favorite destinationfor Japanese tourists. Table 1 shows the top 10 destinations visited by Japanese tourists during2001–2006. The number of Japanese visitors to Taiwan reached a new record of 1.16 millionin 2007.

While it is evident that Taiwan is one of the most popular destinations for Japanese tourists,limited research has been undertaken to analyze the impact of the Severe Acute RespiratorySyndrome (SARS) outbreak on Japanese tourism to Taiwan. Previous studies have found thatthe SARS outbreak, the most catastrophic crisis to hit Taiwan in the past 100 years, has sig-nificant negative impact on the country’s inbound tourism and accommodation stock returns(see, for instance, Chen 2007; Chen et al. 2007a; Kim et al. 2006; Min and Kung 2007).

The purpose of this paper is to use an ARIMA with intervention model (also known asintervention analysis) to examine the impact of SARS on Japanese arrivals to Taiwan. Thismodel would provide some helpful insights for tourism-related decision making and thedevelopment of crisis management strategies.

2 Literature review

When an external incident, such as a natural or man-made disaster, major political or eco-nomic policy initiative, strike, sales promotion, advertising campaign, or new law occurs, itcan be referred to as an intervention. According to Coshall (2003), an improvement in thequality of forecasts can be obtained from univariate time series methods when intervention

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Intervention analysis of SARS on Japanese tourism demand for Taiwan 93

Table 1 Japanese overseas travelers by destination, 2001–2006

No. 2001 2002 2003

Destination No. of travelers Destination No. of travelers Destination No. of travelers

1 USA 4082661 USA 3627264 USA 3169682

2 China 2385700 China 2925553 China 2254800

3 S Korea 2377321 S Korea 2320837 S Korea 1802542

4 Hawaii 1528563 Hawaii 1483121 Hawaii 1340034

5 Hong Kong 1336538 Hong Kong 1395020 Thailand 1042349

6 Thailand 1177599 Thailand 1239421 Hong Kong 867160

7 Taiwan 971190 Taiwan 998497 Guam 659593

8 Guam 901536 Italy 849967 Taiwan 657053

9 Germany 779150 Guam 786947 Germany 646778

10 Singapore 755766 Germany 762471 Australia 627737

No. 2004 2005 2006

Destination No. of travelers Destination No. of travelers Destination No. of travelers

1 USA 3747620 USA 3883906 China 3745881

2 China 3334255 China 3389976 USA 3672584

3 S Korea 2443070 S Korea 2439809 S Korea 2338921

4 Hawaii 1482085 Hawaii 1522356 Hawaii 1362708

5 Thailand 1212213 Hong Kong 1210848 Thailand 1311987

6 Hong Kong 1126250 Thailand 1196654 Hong Kong 1311111

7 Guam 906106 Taiwan 1124334 Taiwan 1161489

8 Taiwan 887311 Guam 955245 Guam 952687

9 Germany 715209 Germany 730232 Germany 759899

10 Australia 710351 Australia 685466 Australia 650900

Source: Japan National Tourist Organization http://www.jnto.go.jp/jpn/tourism_data/data_info_listing.html

analysis is used to capture the impact of a significant intervention. It is a useful techniquewhen the effects of exogenous interventions occurred at some identifiable points in time (Boxand Tiao 1975). Intervention analysis can be treated as an extension of ARIMA modeling,which provides a useful stochastic modeling tool that can be used to rigorously analyze theintervention in the mean level of a time-series. The application of intervention analysis isextensive in the tourism-related literature. Moreover, numerous studies have also applied thetechnique successfully to examine the impact of exceptional external events on variables tobe forecast (Goh and Law 2002).

An important early application of intervention analysis was undertaken by Box and Tiao(1975) who provided an analytical framework for examining the effect of two interventionsin Los Angeles, namely the opening of the Golden State Freeway and the enforcement of anew law concerning oxidant data. An intervention model was used by Bonham and Gangnes(1996) to evaluate the ex post effect of a room tax on hotel revenues in Hawaii in 1987. Theresults showed that there was no statistically significant permanent effect of the room levy oneither the level or growth rate of the after-tax hotel room revenue. A time series interventionanalysis was used to measure the impact and the recovery pattern of the September 11, 2001terrorist attack on US air transport passenger demand by Lee et al. (2005). The findings

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indicated that both US international and domestic air traffic were significantly influenced bythe tragedy for 1–2 months. In Coshall (2003), an intervention model was used to analyze theimpact of three external events on UK air travel and how quickly normal tourist movementresumed. The former includes the US bombing of Libya in 1986, the Lockerbie air disasterin 1988 and the Persian Gulf crisis during 1990–1991. Similar methodology was applied byCoshall (2005) to examine the impact of terrorism, war, and the foot and mouth epidemicon tourist expenditures in the United Kingdom and by UK outbound travelers. Interventionanalysis was implemented to evaluate the effects of smoke-free regulations on restaurant andbar sales in Ottawa City in 2001 by Luk et al. (2006) and the research found no significantadverse impact of the bylaws. The impact of the SARS incident on international visitor arriv-als to China was examined by Chen et al. (2007b) using intervention analysis. Similarly, Minand Kung (2007) and Min et al. (2006) have also used intervention models to examine howTaiwan inbound and outbound tourism demand were affected by the SARS outbreak of 2003.

The forecasting performance of the ARIMA intervention model was compared with othertime series models by Goh and Law (2002) and Lai and Lu (2005). Their studies showed thatthe ARIMA intervention model has outperformed all the other techniques with the lowestforecast error when significant intervention in a series exists. This study will apply inter-vention analysis to assess the impact of the SARS outbreak on Japanese monthly touristarrivals to Taiwan for the period 1979(1) to 2007(12). The rest of the paper is structuredas follows. Section 3 discusses the methodology used to analyze the time series data. Theresults are presented in Sect. 4. Some concluding remarks are given in Sect. 5. The statisticalpackage SAS/ETS version 9.1 is used for the data analysis, intervention model estimationand diagnostic checkings.

3 Methodology

Intervention analysis was originally developed by Box and Tiao (1975). In such an analysis,a time series may be subjected to an external shock or intervention, the impact of whichmay be permanent or temporary, gradual or abrupt. The full intervention impact assessmentmodel may be written as (Yaffee and McGee 2000):

Yt = Nt +∑

t

∑f (It ) (1)

where, Yt denotes the monthly tourist arrivals to Taiwan from Japan; It is the discrete explan-atory (intervention) variable, which is SARS at time t (April 2003), and represents binarydeterministic variables; and Nt denotes the stochastic noise component determined by aunivariate ARIMA model. Equation (1) can be described in two parts as follows.

(i) Noise Indicator

Nt is considered a noise series, representing the background observed series Yt withoutintervention effects and always assumes a (p, d, q)(P, D, Q)s structure, which is a seasonalmultiplicative ARIMA model.

As the model is linear in its components, the noise component may be subtracted fromthe series and yields

(1 − B)d(1 − Bs)D Nt = θ(B)�(Bs)

φ(B)�(Bs)at (2)

where, φ(B) and �(Bs) are the regular and seasonal autoregressive (AR) operators withparameters, φp and �P , respectively. They are represented as polynomials of order p in the

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Intervention analysis of SARS on Japanese tourism demand for Taiwan 95

backward shift operators, B and Bs , and can be described as the effect of past series valuesat lags p. θ(B) and �(Bs) are regular and seasonal moving average (MA) operators withparameters, θ and �, respectively. They are represented as polynomials of order q in thebackward shift operators, B and Bs , and can be explained by the effect of random impacts atlags q. The sample autocorrelation function (ACF) and the partial autocorrelation function(PACF) are examined to identify the AR and MA models. If there is a trend in the series, itis necessary to remove it by applying the differencing filter. D and d are the orders of sea-sonal and regular differencing, respectively. The sequence, at , at−1, at−2, . . ., is said to be awhite-noise process that characterizes independent disturbances and is also called a randomerror. Equation (2) can be represented as:

φ(B) = 1 − φ1 B − φ2 B2 − · · · − φp B p (2a)

�(Bs) = 1 − �1 Bs − �2 B2s − · · · − �P B Ps (2b)

θ(B) = 1 − θ1 B − θ2 B2 − · · · − θq Bq (2c)

�(Bs) = 1 − �1 Bs − �2 B2s − · · · − �Q B Qs (2d)

(ii) Dynamic Indicator

If we have k intervention factors, the extended model may be written as:

Yt =k∑

i=1

vi (B)ξ Ii t +

k+m∑

i=k+1

vi (B)xTit + θ(B)

φ(B)εt (3)

where the superscripts I and T refer to transferable variables, k and m, respectively. ξ Ii t is the

i th intervention series, and stochastic input xTit should be pre-whitened with its own filter.

vi (B) which denotes its impulse function, is given by:

vi (B) = ωi (B)

δi (B)Bb (4)

where, ωi (B) = ω0 − ω1 B − ω2 B2 − · · · − ωi Bs and δi (B) = 1 − δ1 B − · · · − δi Br are si

and ri degrees of B polynomials, respectively. Generally, where the b is pure lag difference,the shock is purely temporary, producing a pulse form:

P(t) ={

0 t �= T1 t = T

(5)

or if it is permanent, producing a step change:

S(t) ={

0 t < T1 t ≥ T

(6)

The step and pulse function are interrelated, and can be expressed as:

P(t) = (1 − B)S(t) (7)

Basically, the simplest analysis consists of using a dummy variable that takes the value 1 atthe time of the intervention and 0 for other times. The intervention is characterized by thestarting point of an event and the expected nature of the impact (also known as the shapeof the intervention model). Extending the above types of intervention responses, Box andTiao (1975) illustrated some typical transfer functions for step and pulse response patternsas shown in Fig. 1.

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96 J. C. H. Min et al.

STEP (T)t

( )S

( )i

i

B

B

ωδ

PULSE (T)t

( )P

( )i

i

B

B

ωδ

(T)tSBω (T)

tBPω

(T)tS

1

B

B

ωδ−

(T )tP

1B

B

ωδ−

(T)tS

1

B

B

ω−

( )1 2

1 1T

t

B BP

B B

ω ωδ

⎧ ⎫+⎨ ⎬− −⎩ ⎭

ωω

1

ωδ−

ω

1ω

2ω

1ω

(a) (d)

(b) (e)

(c) (f)

Fig. 1 Transfer function ωi (B)δi (B)

ξt

While Fig. 1a can be used as a step or abrupt permanent effect with level of magnitudeω, Fig. 1b represents the gradual permanent effect with change rate δ and long-run responselevel ω

1−δ. Figure 1c is a special case of Fig. 1b with δ = 1. An abrupt and temporary effect

with a gradual decay of rate δ that will approach the pre-intervention level with no perma-nent effect is given in Fig. 1d. Figure 1e is similar to Fig. 1d, but with a permanent effectof magnitude ω2. Figure 1e is a linear combination of Fig. 1a, d, with the pattern of Fig. 1abeing equivalent to ωB

1−B P(T )t through the relationship (1 − B)S(T )

t = P(T )t . Figure 1f can be

used instead of Fig. 1e if an initial impact is considered.

3.1 Modeling

The intervention analysis is an interactive procedure for constructing a time series model,and the model building approach can involve three practical steps: identification, estimationand diagnostic checking (Box and Jenkins 1976).

3.1.1 Identification

The initial step in model identification is to undertake a graphical analysis of the data whichwould suggest whether the series is likely to be stationary or nonstationary. In addition, the

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Intervention analysis of SARS on Japanese tourism demand for Taiwan 97

result can be supported by the correlogram which displays the estimated autocorrelation andpartial autocorrelation functions of the residuals.

A tourist arrival series is said to be stationary if the mean, variance and covariance of theseries remain constant over time. The unit root test is a formal method of testing the stationa-rity of a series. A time series yt has a stochastic trend if it contains a unit root. Ignoring theunit root problem in time series would give rise to spurious regressions and incorrect statisti-cal inferences (Nelson and Plosser 1982). The most frequently used method to examine unitroot is the augmented Dickey-Fuller (ADF) test which consists of estimating the followingregression equation:

yt = β0 + αt + β1 yt−1 +p∑

i=1

γiyt−i + εt (8)

where yt is the natural logarithm of monthly tourist arrivals at time t; t is the deterministictime trend; yt−i represent the lagged first differences to accommodate serial correlation inthe errors, εt ; and α, β0, β1 and γ are the parameters to be estimated. The null and alternativehypotheses of a unit root in yt are: H0 : β1 = 0, H1 : β1 < 0. The null hypothesis is basedon the t-statistic (which does not have an asymptotic normal distribution) using simulatedcritical values.

In order to determine p, an initial lag length of 12 is used in the yt regression, andthe 12th lag is tested for significance using the standard asymptotic t-ratio. If the twelfthlag is insignificant at the 5% level, the lag length is reduced sequentially until a significantlag length is obtained. If the null hypothesis of a unit root is not rejected, the time series issaid to be nonstationary. Appropriate regular and/or seasonal differencing are determined totransform the data to a stationary series.

3.1.2 Estimation

In this step, the corresponding parameters of a stationary autoregressive moving average pro-cess are estimated by fitting the model function to the time series. It is based on least squaresand maximum likelihood, involving the minimization of the sum of the squared residual(SSR), defined as:

SS R =n∑

t=1

a2t (9)

3.1.3 Diagnostic checking

After parameter estimation, diagnostic checking is employed by examining the residualsfrom the fitted model to see if the model specification is adequate. The basic assumption isthat {at } is white noise. The Ljung-Box Q-statistic is used to test the adequacy of a modeland it is expressed as follows:

Q = T (T + 2)

K∑

k=1

ρk2

T − k(10)

Q is asymptotically χ2 distribution with k–p–q. If Q < χ2α(k−p−q)(Q > χ2

α(k−p−q)), the nullhypothesis that the model is correctly specified cannot be rejected (is rejected). The iterativecycle of identification, estimation, and diagnostic checking is repeated until a suitable modelrepresentation is found.

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98 J. C. H. Min et al.

year

0

20000

40000

60000

80000

100000

120000

140000

1979

1981

1983

1985

1987

1989

1991

1993

1995

1997

1999

2001

2003

2005

2007

Fig. 2 Japanese visitor arrivals to Taiwan, 1979(1)–2007(12)

4 Results

Intervention analysis begins by identifying a plausible set of ARIMA models. Generally,the longest data span of the pre- and post-intervention observations is used to identify thenoise component Nt (Box and Tiao 1975; Enders 2004). Taking logarithmic transformationof Japanese tourist arrivals for the 29-year period from January 1979 to December 2007,Fig. 2 suggests that the logarithm of tourist arrivals from Japan to Taiwan are likely to benonstationary. The SARS outbreak in April 2003 had a great influence on Japanese touristarrivals to Taiwan, and the former can be treated as an intervention event.

4.1 Pre-intervention model

The appropriate model for Nt is identified prior to the known intervention and the first 291observations, from January 1979 to March 2003, are used for the identification process.Additionally, the ADF test for a unit root is applied, with and without a deterministic trend.The calculated ADF statistic with a deterministic trend (of −3.23) for the series exceeds thecritical value of −3.42 at the 5% significance level. As the null hypothesis of a unit root isnot rejected, this implies that the series is nonstationary. After taking first differences of theseries, the null hypothesis of a unit root is rejected since the ADF statistic (of −7.64) is lessthan the critical value of −3.42 at the 5% level. Hence, the first difference of the logarithmicJapanese tourist arrivals is stationary. Furthermore, the sample autocorrelation for the firstdifferenced series at lags 12, 24, 36, 48 are large, indicating the presence of seasonality in thegiven time series. Seasonal differencing seems to be necessary as the autocorrelations dis-play a distinct seasonal pattern. In view of the sample autocorrelations, both the nonseasonaland seasonal differencing operators are used in the multiplicative form (1 − B)(1 − B12)

to attain stationarity. The appropriate pre-intervention model is determined by checking theACF of the series and the Ljung-Box Q-statistic. The SARIMA model for the pre-interven-tion sample from 1979(1) to 2003(3) is estimated by MLE and the selected model is givenby:

(1 − B)(1 − B12)Zt = (1 − 0.37926B)(1 − 0.61059B12)at (11)

The residual autocorrelations from the fitted model are generally quite small compared withtheir standard errors (see Fig. 3). Hence, the fitted pre-intervention model appears to beadequate.

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Intervention analysis of SARS on Japanese tourism demand for Taiwan 99

Fig. 3 Residual autocorrelation of pre-intervention model

4.2 Full intervention model

In Box et al. (1994), the effects of an intervention are temporary and will die out after timet, and then a pulse function is used. The Japanese inbound series indicates that April 2003 isthe first month the SARS impact started to take effect. Therefore, the intervention variable ξt

is set to take the value 1 at April 2003 and 0 otherwise. According to Fig. 2, the effect of thesingle impulse may last for several months. The subsequent decrease in May 2003 suggesteda numerator lag and the following exponential increase a denominator lag in the transformfunction (Brocklebank and Dickey 2003). An intervention model is of the form: ω0−ω1 B

1−δB ξt

and the fitted full intervention model becomes:

(1 − B)(1 − B12)Zt = (1 − B)(1 − B12)

(ωo − ω1 B

1 − δB

)ξt + (1 − θ1 B)(1 − θ12 B12)at

or Zt =(

ωo − ω1 B

1 − δB

)ξt + (1 − θ1 B)(1 − θ12 B12)

(1 − B)(1 − B12)at

Zt =(−0.86424 − 1.97438B

1 − 0.66791B

)ξt

+ (1 − 0.50595B)(1 − 0.66997B12)

(1 − B)(1 − B12)at

(12)

Table 2 shows that all the estimated parameters are significant with very small p-value. Theestimated residual autocorrelations of the fitted full intervention model illustrated in Fig. 4,appear to be random and are within the 95% confidence interval. The Ljung-Box Q statisticsare not significant, which implies that the full intervention model is adequate. A graphicpresentation of the percentage of post-intervention effects is given in Fig. 5.

The SARS outbreak is seen as an intervention event on the Japanese arrivals to Taiwan.As shown in Fig. 5, Taiwan’s inbound tourism from Japan was immediately and severelyaffected by the epidemic. In particular, the impact (in percentages) was considerable during

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100 J. C. H. Min et al.

Table 2 Maximum likelihood estimates of fitted full-intervention model

Parameter Estimate Standard error t value p-value Lag Variable

θ1 0.50595 0.04725 10.71 <0.0001 1 MA(1)

θ12 0.66997 0.04341 15.43 <0.0001 12 MA(12)

ωo −0.86424 0.09080 −9.52 <0.0001 0 SARS

ω1 1.97438 0.09453 20.89 <0.0001 1 SARS

δ 0.66791 0.02403 27.79 <0.0001 1 SARS

Fig. 4 Residual autocorrelation of intervention model

-100.00%

-80.00%

-60.00%

-40.00%

-20.00%

0.00%

month

the

% o

f im

pact

the % of impact -57.86% -92.20% -81.81% -67.96% -53.25% -39.82% -28.76% -20.27% -14.04% -9.61% -6.53% -4.41%

Apr-03 May-03 Jun-03 Jul-03 Aug-03 Sep-03 Oct-03 Nov-03 Dec-03 Jan-04 Feb-04 Mar-04

Fig. 5 Post-intervention effects on Japanese tourist arrivals (%)

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Intervention analysis of SARS on Japanese tourism demand for Taiwan 101

the first five months (from April to August 2003), representing more than 50% decline intourist arrivals on average per month. Apparently, the World Health Organization (WHO)most stringent world-wide warning in May 2003 to avoid traveling to Taiwan had contributedto the drastic decline in tourist arrivals from Japan by more than 92%. The WHO removedTaiwan from its SARS travel advisory list and SARS-affected regions in June and July2003, respectively (Taiwan Tourism Bureau 2004). Consequently, Japanese inbound tourismimproved steadily from July 2003. Although the health-related incident had impeded theflow of Japanese tourists to Taiwan, inbound traffic from Japan had almost returned to thepre-SARS level a year after the incident, representing the pulse impact of the catastrophe onJapanese tourist arrivals.

5 Conclusion

In this study, we have estimated the univariate time series SARIMA intervention model toevaluate the impact of SARS on Japanese tourism flows to Taiwan and Japanese tourismdemand in the aftermath of the SARS outbreak. The empirical results show that inboundtourism from Japan has been severely affected by the communicable viral disease. Contraryto the studies by Lim et al. (2008, 2009) in which SARS did not have a significant effecton Japanese tourist arrivals to Taiwan, the current study showed that SARS has underminedJapanese inbound tourism, and its impact on tourism demand lasted for about a year.

There is no doubt that international tourism flows can be significantly affected by naturaland/or man-made events. It is of paramount importance for crisis management that destina-tion governments undertake research to analyze the effects of disastrous events on tourism.In particular, tourism has been proven to be sensitive to numerous impacts from internal andexternal environmental factors which might disrupt its operation (Henderson and Ng 2004).The contribution of the current study would be to use intervention analysis to evaluate theimpact of the SARS crisis on Japanese visitor arrivals to Taiwan. Moreover, the findings ofthe study provide some insight for tourism planning and management of products such asinfrastructure, airline seats and accommodation, to help the industry respond to the impact ofexogenous shock and sudden downturn in tourism demand. Future research will includeestimation and testing of alternative models for forecasting Japanese outbound tourismto Taiwan.

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