co-integration analysis of quarterly european tourism demand in tunisia

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Tourism Management 29 (2008) 127–137

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Co-integration analysis of quarterly European tourismdemand in Tunisia

Chokri Ouerfelli1

Department of Quantitative Methods, I.S.G., University of Gabes – Tunisia, Rue Jilani Lahbib, 6002 Gabes – Tunisia

Received 10 May 2006; received in revised form 4 February 2007; accepted 12 March 2007

Abstract

The purpose of this study is to identify the factors that affect the destination choice process. In addition to prices and income factors,

the supply factor is introduced as an explanatory variable in the econometric model. Co-integration analysis and error correction models

(ECMs) are used to estimate the long run tourism demand elasticities and to forecast the quarterly European tourism demand for a

1-year-ahead horizon. The main finding of this study is that the behaviour of European tourists varies from one country to another. The

co-integrating relationships show that the large elasticity magnitude may be the reflection of the relatively expensive services often sought

after by tourists from these countries. The estimated values of the supply elasticity corroborate the supply induced demand hypothesis.

Finally, compared to the basic structural model and using the root mean squared error, the ECM provides more precise forecasts.

r 2007 Elsevier Ltd. All rights reserved.

Keywords: Supply induced demand; Seasonality; Cointegration; Error correction model; Elasticity; Root mean squared error

0. Introduction

Tourism plays an important role in Tunisia’s economicdevelopment because of its contribution towards balancingthe commercial deficit and to cutting unemployment. Since1986, the tourism industry has become the second largestforeign currency earner after the textile industry. Thissector shows a strong seasonal fluctuation that results in aconcentration of the demand during certain months of theyear, particularly in July, August and September. It isessentially the seaside character of Tunisian tourism thatattracts people during the high season. The under-usage ofthese tourist sites during the off-season has a negativeimpact on the financial performances of this sector.

The purpose of this paper is to identify the factors thataffect the destination choice process. The cost of tourismand the income level are the tourist demand determinants(Lim, 1999). However, in a difficult international con-

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urman.2007.03.022

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juncture, and with increasingly aggressive competition,tourism operators may need attractions other than seasideto bring in more tourists, particularly off-season. To targetdifferent types of tourists they have developed other kindsof products and services, such as cultural heritage, and/ortourism for other motives like business, health programs orsports. It would be appropriate to consider using thesupply factor to explain the tourism demand. In this study,we will give an empirical justification of the supply induceddemand hypothesis.Seasonally non-adjusted quarterly data of European

tourist arrivals are used from 1981 to 2005. It is known thateconomic data is often non-stationary, in particular, highfrequency data. Tourism is a seasonal activity and as suchdata may exhibit non-stationary trends and seasonality;as a result, the traditional least square regression approachwill lead to erroneous results (Franses, Hylleberg, & Lee,1995; Granger & Newbold, 1974). If we consider the seasonaland non-seasonal stationarity of the series, cointegrationanalysis is a suitable strategy to model and forecast thetourism demand for the following reasons. First, using thedifference filters (i.e. seasonal and non-seasonal) proposedby Box and Jenkins to achieve stationarity leads to a loss of

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ARTICLE IN PRESSC. Ouerfelli / Tourism Management 29 (2008) 127–137128

information about the long term relationships betweennon-stationary economic series (Box & Jenkins, 1976). Theerror correction models (ECMs) provide a way to avoidthis problem because the long run information lost due todifferentiating is reinstated in the ECMs. Second, since theexistence of unit-roots tests of Hylleberg, Engle, Granger,and Yoo (1990) (HEGY), the empirical studies using thisprocedure show, in most cases, that the hypothesis of unitroot is rejected at least at one frequency, so the systematicapplication of the seasonal difference may generate anoverdifferentiation problem (Bell, 1987; Hylleberg, Engle,Granger, & Yoo, 1990). Third, the ECMs provide a way tocombine both dynamics of short run and long runadjustment processes simultaneously (Dritsakis, 2004;Dritsakis & Papanatasious, 1998; Gonzalesz & Moral,1995; Kim & Song, 1998; Kulendran & Witt, 2001).

In this study, the Johansen (1988) and Johansen andJuselius (1990) methods are used to estimate long runtourism demand elasticities. ECMs are then estimated andused to forecast the quarterly TArr from the 4 mostimportant European countries and compute the estimatedstatistics. After having shown the place of Europeantourism in the Tunisian economy and its evolution duringthe last three decades, Section 2 emphasizes the relevantfactors that influence the destination choice process. Thetheoretical framework of analysing the tourism demandwill then be discussed. The empirical results of thecointegration analysis and the commentaries will be care-fully dissected in the third section. The ECMs are used inthe final section to forecast the quarterly European TArr inTunisia. Their forecasting performances are compared tothose of the basic structural model (BSM) using the rootmean squared error (RMSE).

1. Determinants of the tourism demand

A large amount of literature has been published ontourism demand forecasting using econometric techniques.These studies include, among others, Dritsakis (2004),Song, Witt, and Jensen (2003), Hiemstra and Wong (2002),Tan, McCahon, and Miller (2002), Kulendran and Witt(2001), Smeral and Weber (2000), Song and Witt (2000),Kulendran and King (1997), Marley (1994), Martin andWitt (1989), Witt and Martin (1987). These studies showthe importance of using econometric models to identify thetourism demand factors and then to generate demandelasticities and forecasts. Before identifying the Europeantourism demand factors, it is advisable to consider theEuropean market in the light of the current changes in theTunisian tourism sector.

1.1. The place of the European market in Tunisian tourism

Between 1980 and 2004, investment in the tourismindustry rose from 31,638 (million Tunisian dinars: MD) to288,185 MD with an approximate average annual growthrate of 9.24%, whereas, tourism based employment grew at

an average rate of 4.71% per annum. The currencyexchanged during the same period covered was on averageabout 53% of commercial deficit with exceptional resultsfrom 1987 to 1990. With such a performance, the tourismindustry makes up an average of 6% of the GDP.In this study, four main countries are considered:

Germany, France, United Kingdom and Italy. Thesehighly developed countries with strong currencies (com-pared to the Tunisian dinar) accounted for about 75% ofTArr from Europe, more than 67% of the EuropeanTourist bed-nights and about 60% of the total touristexpenditure in 2004 (63.23% in 2002). This places Tunisiain a strong position compared to many other rivaldestinations.Furthermore, the long lasting economic relationship

between Tunisia and Western Europe makes this region themost important commercial partner. This market, diversi-fied and vast (i.e. Western Europe), guarantees a promisingfuture in the present economical and political conjunctures(the European Union of 25 countries). Finally, this study islimited to the most important countries in order to obtainhomogeneous and accurate results necessary for a reliableanalysis. In the following paragraph, the factors which mayexplain tourist destination choice will be presented.The dependant and the explanatory variables are thendeduced.

1.2. The tourism demand factors

The expansion of tourist services demanded in Tunisia isthe consequence of many factors. Tourism in Tunisia ismainly seaside but cultural tourism and Spa resorts are alsobeing developed.The following identification of these factors is useful for

two reasons. First, it provides researchers with theinformation on how tourists finalize their destinationchoice. It can also allow forecasters to assess the manner(direction and magnitude) in which tourists would respondgiven any changes in the determining factors by examiningthe estimated demand elasticities. Secondly, these factors,used in econometrics models, can help policymakers createeconomic strategies in order to influence the tourismdemand (Witt & Witt, 1995).

1.2.1. Quantification of the tourist demand

The international tourism demand is often measuredeither in terms of the number of tourist arrivals, touristbed-nights and/or in terms of tourist expenditure in thedestination country. The aim of decision-makers is to havemore tourists in Tunisia mainly in the off-season. There-fore, it seems reasonable to quantify the tourist demand byquarterly tourist arrivals (TArr).

1.2.2. Determinants of tourism demand

The diversity of economic and non-economic factorsthat constitute the structure of the tourism sector illustratethe complexity of the identification process. To make this

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2Johnson and Thomas (1995) highlighted the negative impacts of the

hypothesis of an infinitely elastic tourist supply under the neoclassic

assumption of the independence of supply and demand.

C. Ouerfelli / Tourism Management 29 (2008) 127–137 129

process feasible, only the factors which can be measured willbe shown in this analysis. In a recent study of 100 papersabout tourist demand factors, Lim (1999) found that the mostcited explanatory variables of tourist demand are income(84%), relative prices (74%) and transport costs (55%).

Regarding the characteristics of European tourists (i.e.travelling habits, motivations, expectations, etc.) and theperception of Tunisia, the tourism demand factors includetourism cost, income level, and supply of tourist services.The latter consists notably of natural heritage (climate,sunny beaches) and hotel capacity (luxurious hotels,holiday villages etc.). In fact, the own price and substituteprice elasticities can provide useful suggestions forthe formulation of pricing and competition strategies.Income elasticity enables professionals to measure theimpact (on tourism demand) of a change in revenuedistribution in the origin countries (see Crouch, 1992; Song& Wong, 2003).

1.2.2.1. The income level. In many European countries,with a high standard of living, leisure spending consump-tion takes an important place in the domestic budget. Aftercovering ‘‘primary’’ needs, the remaining income is usuallydedicated to leisure. This factor seems to be suitablymeasured by the disposable income level, however, becauseof the problem of data unavailability, the gross domesticproduct per capita (GDP) is used to measure the incomevariable.

1.2.2.2. The own price. This factor should include tour-ists’ living costs and travel costs to Tunisia. However, dueto the very strong competition between transport compa-nies, travel cost data are unavailable. Indeed, the packagetour formula, provided by tour operators, makes the travelcost variable insignificant. A measure of the price oftourism services will be the consumer price index (CPI)adjusted by the exchange rate (ER).

The own price (P) is then given by

P ¼CPIT

ERi

; lnP ¼ lnCPIT � ln ERi

Where CPIT is the consumer price index of Tunisia andERi is the exchange rate of the origin country’s currency i

(i ¼ France, Germany, United Kingdom and Italy) interms of the Tunisian Dinar. The logarithm of this variableis given by the logarithm of the CPI minus the logarithm ofthe exchange rate. This variable (i.e. the own price)measures the effective price of goods in Tunisia expressedby the number of units of the origin country’s currency.

1.2.2.3. The substitute price. The tourism industry inTunisia must compete with other destination countriesespecially those who offer the same products and services.These include Egypt, Turkey, Morocco, Malta and Cyprus.The potential tourist often compares prices for eachdestination before making a choice. A proxy of the costof tourism in these countries (i.e. the substitute price: SP) is

the weighted average of the consumer price index (CPI) ofthese destinations which allows for substitution possibili-ties between them:

SP ¼X5j¼1

aj

CPIj

ERj

CPIj and ERj are, respectively, the consumer price indexand the exchange rate of the currency of the rival country j,j ¼ 1; . . . ; 5.

aj ¼TArrjP5j¼1TArrj

;

TArrj designates the European tourist arrivals in country j.

1.2.2.4. Tourist offer factor. Favourable natural andclimatic conditions and/or rich cultural heritage do notautomatically guarantee the choice of a destination. Toassure client loyalty, tourism operators must guarantee anadequate infrastructure and most importantly hospitality.The Tunisian tourist package is essentially composed of

accommodation and transport. Hotel capacity is animportant component of the tourist supply. It may affectthe potential demand in two ways: (i) it reflects theproduct’s quality and expresses the destination’s notoriety;and (ii) the quality and the quantity of this variable can bedecided by the tourism professionals and managedaccording to tourist expectation.2

A proxy of the hotel capacity is the accommodationcapacity (in beds: AC) given by the following formula:

AC ¼Total number of beds

Total number of accommodations.

The supply variable used in this study reflects not onlythe accommodation capacity of Tunisian sites but alsoreflects the hotel infrastructure investment of the entrepre-neurs in the tourism sector. Other services, such asdistraction sports and cultural activities, are not included.Empirically, it is not only difficult to quantify these servicesby a synthetic variable but also impossible to find data.

1.2.2.5. The seasonal factor. The tourism sector shows astrong seasonal pattern that results in a concentration ofthe demand during certain months of the year, particularlyJuly, August and September. It is essentially the result ofTunisian’s seaside character that attracts people during thehigh season. The under-usage of tourist sites during the off-season has a negative impact on the financial performancesof this sector. To minimize this downturn, tourismoperators offer off-season price advantages to touristsvisiting Tunisia in order to spread demand throughout theyear. They have also been diversifying services by devel-oping other kinds of tourism in order to target moretourists.

ARTICLE IN PRESSC. Ouerfelli / Tourism Management 29 (2008) 127–137130

They create programs aiming to

�
target consumers who can travel throughout the year(guests, attendees, etc.); � differentiate services, such as developing other kinds of
tourism : cultural, business, etc., where the climate is notnecessarily the main attraction.

Many recent empirical results show that the seasonalityof many tourist series changes over time. Indeed, using theapproach of Hylleberg, Engle, Granger, and Yoo (1990)for monthly Tunisian tourist data, the null hypothesis ofseasonal unit roots is not rejected for several frequencies(Ouerfelli, 2005). Thus, it is necessary to model thiscomponent in the seasonal econometrics models. Suitablestatistic tests will be applied to identify the aspect of thiscomponent in the data.

1.2.2.6. Other factors. There are a few unpredictablevariables in Tunisia that may influence tourism demandsuch as the advertising and marketing budget, touristeducation, security at the destination, and other variablesthat depend on knowledge of consumer types andmotivation. These variables may have been intentionallyexcluded because of the lack of data available and/or thedifficulty in measuring them.

1.3. The sample

Tourist data was obtained from an annual document‘‘Le tourisme tunisien en chiffre’’ published by the TunisianNational Tourist Office (TNTO). The economic data wascollected from Eurostat ‘‘Quarterly National Accounts’’and the International Financial Statistics. These combineddata from 1981:1 to 2004:4 and included: quarterly dataabout Tourism arrivals (TArr), the income level (I), theown price variable (P), the accommodation capacity (AC)and the substitute price variable (SP).

The exchange rate is the quarterly average market rate ofthe local currency against the US dollar.

Logarithmic transformations, which are used to expressthe multiplicative in the level of the variable, are appliedand the transformed data is plotted (see Fig. 1).

Note the three important dips in the tourist activity forthe periods 1982–86, 1987 and 1991, respectively. The firstis due to the economic crisis during the period 1982–86,where the reduction of tourism was 2%; the Germanand the English markets seemed to be the most affected.The second is due to the terrorist attacks in some touristregions during the summer of 1987; the French marketwas the most affected by these incidents. The thirdexpresses the negative impact of the Gulf war, when thenumber of TArr from the four origin countries droppedsignificantly. The basic structural model and the Harveyprocedure is used to forecast the aberrant data of 1991(Harvey, 1990).

2. Modelling the European tourist demand

The literature on tourism demand analysis can bedivided into two main groups. The first group focuses onthe non-causal (mainly time series) modelling approachwhile the second group is based on causal (econometric)methods. The forecasting based on non-causal modellingapproaches ‘‘extrapolates the historic trends into the futurewithout considering the underlining causes of the trends’’(Song et al., 2003, p. 437) (e.g. Box-Jenkins ARIMA modeland the exponential smoothing method). Causal forecast-ing models include the factors that influence tourismdemand, so that they can be used by decision-makers forpolicy evaluation purposes. Furthermore, the touristdemand model must take into account the time path ofthe tourist’s decision-making process (Song & Witt, 2000,p. 28). When non-stationary variables are used, the errorcorrection representations offer an alternative approachto modelling integrated data. They associate two kindsof variables: the co-integrated non-stationary variablesand the other stationary variables such as the growthrate of the dependant variable and (or) the exogenousvariables.In order to assess the relative explanatory power of the

exogenous variables, it is suggested that insignificantvariables be deleted until a parsimonious representationis obtained and the OLS model is implemented.Regarding the German tourist demand, the results show

that TArr can be better explained by the GDP, theTunisian CPI, the AC, the SP and the ER:

TArr ¼ �23:88ð�7:69Þ

þ 3:71GDPð5:71Þ

þ 3:54ACð13:45Þ

� 7:47CPIð�9:37Þ

þ 0:43 SPð3:91Þ

þ 1:77ERð6:91Þ

,

R2 ¼ 0:86; DW ¼ 1:29; Qð20Þ ¼ 102:90.

The ER variable is not a statistically significantexplanatory variable of the TArr from France:

TArr ¼ �33:71ð�3:06Þ

þ 2:77GDPð2:01Þ

þ 2:67ACð7:18Þ

� 2:71CPIð�5:40Þ

þ 0:30 SPð2:30Þ

,

R2 ¼ 0:62; DW ¼ 1:99; Qð20Þ ¼ 578:20;

AIC ¼ �0:699; BIC ¼ 0:833.

Regarding the Italian tourist demand, two OLS modelsare estimated:

ð1Þ TArr ¼ �29:45ð�2:98Þ

þ 2:17GDPð1:24Þ

þ 3:25ACð7:11Þ

� 2:43CPIð�2:79Þ

þ�0:15 SPð�0:85Þ

;

R2 ¼ 0:75; DW ¼ 1:82; Qð20Þ ¼ 135:43,

AIC ¼ 1:125; BIC ¼ 1:262,

ARTICLE IN PRESSC. Ouerfelli / Tourism Management 29 (2008) 127–137 131

ð2Þ TArr ¼ �28:94ð�2:94Þ

þ 1:81GDPð1:07Þ

þ 3:28ACð7:28Þ

� 2:39CPIð�2:76Þ

,

R2 ¼ 0:74; DW¼ 1:81; Qð20Þ ¼ 134:34; AIC ¼ 1:112,

BIC ¼ 1:222.

The TArr variable for the UK seems to be explained bythe GDP, the P and the SP: (1) if a stochastic seasonality is

Tunisian market

10.8

11.2

11.6

12.0

12.4

82 84 86 88 90 92 94 96 98 00 02 04

The Hotel Capacity

1. The French market

10.5

11.0

11.5

12.0

12.5

13.0

82 84 86 88 90 92 94 96 98 00 02 04

Tourist Arrivals from France

2

4

6

8

10

12

82 84 86 88 90 92 94 96 98 00 02 04

Exchange Rate

2. The German market

10.5

11.0

11.5

12.0

12.5

13.0

82 84 86 88 90 92 94 96 98 00 02 04

Tourist Arrivals from Germany

0.91.01.11.21.31.41.51.6

82 84 86 88 90 92 94 96 98 00 02 04

Own Price

Fig. 1

included as suggested by Harvey (1990):

TArr ¼ �0:071D02ð�1:62Þ

þ 0:017D03ð3:87Þ

þ 0:071D04ð1:60Þ

þ 1:44GDPð24:09Þ

� 0:93Pð�6:29Þ

þ 0:003 SPð0:03Þ

R2 ¼ 0:73; DW ¼ 0:31; Qð20Þ ¼ 268:5

4.4

4.6

4.8

0

5.2

5.4

5.6

5.8

6.0

82 84 86 88 90 92 94 96 98 00 02 04

Consummer Price Index

9.5

9.6

9.7

9.8

9.9

10.0

82 84 86 88 90 92 94 96 98 00 02 04

Gross Domestic Product

9.5

9.6

9.7

9.8

9.9

10.0

82 84 86 88 90 92 94 96 98 00 02 04


2

4

6

8

10

12

82 84 86 88 90 92 94 96 98 00 02 04

Exchange Rate

.

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3. The English market

9.5

10.0

10.5

11.0

11.5

12.0

82 84 86 88 90 92 94 96 98 00 02 04

Tourist Arrivals from The UK

-0.8

-0.6

-0.4

-0.2

0.0

0.2

82 84 86 88 90 92 94 96 98 00 02 04

0.4

0.6

0.8

1.0

1.2

82 84 86 88 90 92 94 96 98 00 02 04

Exchange Rate

6.97.07.17.27.37.47.57.6

82 84 86 88 90 92 94 96 98 00 02 04


4. The Italian market

8

9

10

11

12

13

82 84 86 88 90 92 94 96 98 00 02 04

Tourist Arrivals from Italy

7.5

7.6

7.7

7.8

7.9

8.0

8.1

82 84 86 88 90 92 94 96 98 00 02 04


6.8

7.0

7.2

7.4

7.6

7.8

82 84 86 88 90 92 94 96 98 00 02 04

Exchange Rate

5.2

5.4

5.6

5.8

6.0

6.2

6.4

6.6

82 84 86 88 90 92 94 96 98 00 02 04

Substitute Price

Own Price

Fig. 1. (Continued)

C. Ouerfelli / Tourism Management 29 (2008) 127–137132

Where Dj0 ¼ (Dj�D1) j ¼ 2,y, 4 and Dj are the seasonal

dummies.

ð2Þ TArr ¼ 0:65TArrð�4Þð8:98Þ

þ 0:48GDPð4:03Þ

� 0:41Pð�2:99Þ

þ 0:06 SPð0:61Þ

,

R2 ¼ 0:82; DW ¼ 0:56; Qð20Þ ¼ 104:94,

AIC ¼ �0:345; BIC ¼ �0:233.

The Akaike information criterion (AIC) and SchwartzBayesian Criterion (BIC) are useful measures of goodnessof fit. The model with the smallest AIC and BIC values ispreferred.

The estimated values of DW and the QLB statistics showa strong residual autocorrelation probably due to the non-stationarity of the data.

Indeed, an eventual stochastic seasonal non-stationarityof the TArr variable implies that using the OLS methodwill hold spurious results, that is why the structural timeseries model and the Harvey method are used to estimatethe econometric models for Germany and the UK (see alsothe simulation works of Franses et al., 1995).

2.1. Error correction models

In this study non-differentiated variables are used and theECMs are considered to accommodate the non-stationaryfeatures of the data. We shall begin with testing for unitroots at zero and seasonal frequencies. The augmentedDickey and Fuller test and the HEGY procedure areapplied to test for the existence of stochastic trends andnon-stationary stochastic seasonality, respectively.


2.1.1. Unit root tests

The non-stationarity of the data is probably due to thepresence of long run and seasonal unit roots which impliesthat, in addition to a stochastic trend, these series exhibit avarying seasonality. The procedure, shown in this para-graph, was used to test for non-stationarity in each series inorder to check for stationary demand relationshipsbetween these series.

2.1.1.1. Augmented dickey and fuller tests. To test for thelong run frequency, Dickey and Fuller (1979) proposed aprocedure based on the following auxiliary regression:

Dyt ¼ aþ btþ dyt�1 þXk

j¼1

gjDyt�k þ �t, (3)

where Dyt ¼ (1�L) designates the first difference filter, et isthe error term and a, b and d are the parameters to beestimated.

2.1.1.2. HEGY tests. The seasonal pattern of a series canchange over time. Hence, the series exhibit non-stationaryseasonality. A simple model that can describe the variationof the series is the seasonal random walk model given by

yt ¼ yt�s þ �t.

This model assumes s unit roots at seasonal frequencies.The series yt is then an integrated seasonal process at thecorrespondent frequency oj ¼ 2pj/s, j ¼ 1,y, s/2, notatedIoj(1) where s is the number of time periods in a year. Ifs ¼ 4, then the series has four roots with modulus one: oneat a zero frequency, one at p (two cycles per year) and p/2(one cycle per year). Evidence of unit roots at seasonalfrequencies implies that the stochastic seasonality is non-stationary. Hylleberg, Engle, Granger, and Yoo (1990)proposed a strategy that tests for unit roots in quarterlydata (i.e., to deduce the appropriate difference operatorthat must be applied to the series to achieve stationarity).

The test equation for the presence of seasonal unit rootsis given by

FðLÞy4t ¼ p1y1;t�1 þ p2y2;t�1 þ p3y3;t�2 þ p4y3;t�1

þ mt þ �t, ð4Þ

where yit ¼ ji(L)yt for i ¼ 1; . . . ; 3:j1(L) ¼ (1+L+L2+L3), j2(L) ¼ �(1�L+L2

�L3),j3(L) ¼ �(1–L2), j4(L) ¼ (1�L4). The deterministiccomponent mt includes seasonal dummies, a trend and aconstant term, and et is a normally and independentlydistributed error term with a zero mean and constantvariance.

Testing for unit roots implies testing the significance ofthe estimated pi. The null hypothesis pi ¼ 0, i ¼ 1,y, 4,implies that there is a unit root at the zero and semi-annualand annual frequencies, and it is appropriate to applythe (1�L4) filter to achieve stationarity. The tests for p1and p2 are one-sided while the tests for the other pi aretwo-sided.

2.1.2. Cointegration analysis

When the series are an integrated process at zero and/orat seasonal frequencies, difference filters can be used toachieve stationarity. The obtained stationary series canthen be modelled with suitable econometric models.If some linear combinations of these series are notintegrated then another approach consists of using error-correction representations to model the dependant variablewith the supposed cointegrated series (see Dritsakis, 2004;Kulendran & Witt, 2001; Lim & McAller, 2001).Inspired by Johansen and Juselius’s (1990) approach and

that of Lee (1992), Johansen and Schaumburg (1998)presented a maximum likelihood estimation procedure forseasonally cointegrating vectors (CV). The Johansen andJuselius’s (1990) full-information maximum likelihood isdeveloped in the following paragraph to test for cointegra-tion and to estimate, if necessary, the long run equilibriumrelationships.

2.2. Basic structural models

The structural model can be written as the followingmathematical function (Eq. (1)):

yt ¼ mt þ St þ x0tdþ �t; t ¼ 1; . . . ;T , (2.1)

where, yt is the dependant variable at time t, mt and St

are the trend and the seasonality components ; they aregiven as

Djt ¼

1; t ¼ j; j þ s; j þ 2s; . . . ;

0; taj; j þ s; j þ 2s; . . . ;

1; t ¼ s; 2s; 3s; . . . ;

8><>:

j ¼ 1; . . . ; s� 1,

s is the number of seasons, in this study s ¼ 12.We add the hypothesis that

gt ¼ �Ps�1

j¼1gt�j þ ot; ot�Nð0; s2oÞ;

mt ¼ mt�1 þ Zt; Zt ! NIDð0; s2ZÞ;

xt is the explanatory variable vector, d is the unknownparameter vector.The error processes et, xt, Zt and ot are mutually

independent, and where NID designates normally andindependently distributed.

3. Empirical results

In this section, once a preliminary test for the order ofintegration is applied to the series, the estimation of long-run relationships is provided. The ECMs are then deducedand used to forecast the quarterly tourism demand.

3.1. The unit-roots test results

Using the Eviews 5 software package, the ADF tests areapplied to the logarithms of all the series to estimate thetest Eq. (4) where the order of the autoregressiveaugmentation is chosen in an experimental way. The tests

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Table 1a

The unit roots tests results

Countries France Germany UK Italy

Statistics TArr I P SP TArr I P SP TArr I P SP TArr I P SP

ADF-stat. I(1) I(0) I(0) I(0) I(1) I(1) I(1) I(0) I(1) I(1) I(0) I(1) I(1) I(1) I(0) I(0)

0 I(1) I(0) I(1) I(1) I(1) I(1) I(1) I(0) I(1) I(1) I(0) I(1) I(1) I(1) I(1) I(1)

p I(1) I(0) I(0) I(0) I(1) I(0) I(0) I(0) I(0) I(0) I(0) I(1)a I(1) I(0) I(0) I(1)a

p/2 I(1) I(0) I(0) I(0) I(1) I(1) I(0) I(0) I(1) I(0) I(0) I(0) I(1) I(0) I(0) I(0)

Diagnostics

Q(30) 12.7 23.8 12.9 18.9 21.6 13.1 20.5 18.6 14.8 19.7 14.63 20.72 8.3 15.6 23.0 15.4

JB 36.5 0.3 117 37.4 12.1 2734 46.1 33.3 9.7 9.4 9.30 4.58 69.7 0.30 38.5 42.8

BG 1.6 0.7 0.3 0.16 0.9 0.45 0.9 0.00 0.31 0.31 0.09 0.95 2.5 0.16 0.07 0.18

In bold, non-significant values at 5% level, (the critical values (c. v. 5%) are taken from Hylleberg, Engle, Granger, and Yoo (1990) for 120 observations).

An intercept, 4 seasonal dummies and a time trend are included in the auxiliary regression.aThe integration at the frequency p is rejected at 10% level. This hypothesis is also rejected if we consider the other auxiliary regression.

Table 2

The percentage of TArr to each destination from country i (i ¼ 1,2,3,4)

Origin

country

Cities

Tunis Zaghouan Hammamet Sousse Djerba Tozeur

Year 2003 2004 2003 2004 2003 2004

Germany 4.76 5.04 56.36 54.32 38.87 40.63

UK 4.65 4.80 76.49 79.82 18.86 15.37

France 9.80 10.06 27.91 27.15 62.29 62.79

Italy 9.81 9.02 27.50 29.63 62.69 61.35

Table 1b

Statistics ADF-stat. HEGY-test Diagnostic

0 p p/2 Q(20) JB BG

AG I(1) I(1) I(1) I(1) 6.72 57.74 2.79

CPI I(1) I(1) I(0) I(0) 6.65 3.47 0.50


for p1 and p2 are one-sided while the tests for p3 and p4 aretwo-sided using the Wald test. The diagnostic tests used arethe Ljung–Box (Q(k)) and the Lagrange multiplier (LM(c))for serial correlation, and the Jarque–Bera Lagrangemultiplier test for normality (LM(n)).

The results are given in Tables 1a and 1b; they show thatthe hypothesis of root 1 is accepted at a 5% level for all theseries. They also show that the hypothesis of unit root isnot rejected for at least one frequency for all the series withthe exception of the GDP for France, the Germany’s SPand P for the UK. Strictly speaking, evidence of anintegration at the zero frequency for almost all the seriesimplies that they have non-stationary stochastic trends.Furthermore, the integration at the semi-annual andannual frequencies implies that they exhibit non-stationarystochastic seasonality as it is the case of the TArr and theAC series. However, the results show no stochasticseasonality in all other series with the exception of SPwhich is integrated at the semi-annual frequency for bothUK and Italy. Note that this null hypothesis of integrationis rejected at a 10% significance level, therefore, only thelong run cointegration will be studied in this paper.

3.2. Long-run cointegration

In order to run the cointegration test at the zerofrequency, seasonal difference filters are applied to removethe roots at seasonal frequencies from the non-stationaryseries. The filter (1+L) is applied to the SP series and theS(L) ¼ (1+L+L2+L3) is applied to the other seasonal

series. The following test equation is used.

DY t ¼ mþ FDt þPpY t�p þXp�1

i¼1

PiDY t�i þ vtðt ¼ 1; . . . ;TÞ;

(5)

where Yt is the vector of n non-stationary series, m and Dt

are the constant term and the three centred seasonaldummies, respectively; v1; . . . ; vT are I.I.d. Nn(0, L).If a set of n I(1) variables has r cointegrating vectors,

then the system will have n–r common stochastic trends(Engle & Granger, 1987).For each origin country, the cointegration relationships

are estimated. These long run equilibrium are included inthe ECM to forecast tourist demand. Eviews 5.0 is used todeduce the log-likelihood ratio statistics to compute thenumber, r, of long-run cointegration relationships for eachcountry. Using the AIC and the Lung-Box-Q statistics, anautoregressive correction of order p ¼ 2 is obtained. Theresults are given in Table 2.The results show multiple statistically significant long-

run relationships. The individual coefficients cannot easilybe interpreted because the CVs are not identified withoutprior information (Wickens, 1996). However, Muscatelliand Hurn (1992) and Kunst (1993) have suggestedchoosing a relationship where the long-run coefficientscorrespond in both sign and magnitude to the economic


theory. If the estimated long-run tourist demand relation-ships are considered the statistically significant individualcoefficients designate long-run tourist demand elasticities.

The likelihood ratio (LR) test indicates the cointegratingequations at a 5% significance level.

For Germany, the LR test indicates one cointegratingrelationship

SðLÞTArr ¼ 41:45þ 1:47 I � 5:17P:

For France, the LR test indicates three significantcointegrating relationships

TArr ¼ � 37:63þ 4:66 I � 2:52CPI

þ 1:56AC� 0:07 SP;

TArr ¼ � 40:89þ 3:73 I � 2:51CPI

þ 2:19ACþ 0:73 SP;

TArr ¼ � 60:84þ 4:51 I � 4:89CPI

þ 4:48ACþ 0:38 SP:

For the UK, the LR test indicates one significantcointegrating relationship as follows:

SðLÞTArr ¼ 30:831þ 0:76 I � 8:34Pþ 1:23 SP:

For Italy, the LR test indicates four significant coin-tegrating relationships, however, only one can be retained

TArr ¼ � 34:63þ 3:64 I � 1:51CPI

þ 2:16AC� 0:06 SP:

The income and the relative prices are highly elastic asindicated by the estimated long run elasticities. Indeed, thehigh significant estimated value of the AC elasticity showthe importance of the supply variable in the demand modelfor France and Italy and corroborate the supply induceddemand hypothesis. This variable is not statisticallysignificant at a 5% significant level if we consider Germanyand the UK.

Furthermore, the income coefficients suggest that holi-days in Tunisia are regarded as a luxury by tourists fromFrance and Italy (4.00 and 3.64, respectively). By contrast,the income coefficient in the German and the UKequations (i.e. 1.47, 0.76) suggest that holidays in Tunisiaare regarded as a necessity because sunny beaches, dunes,oases, spa resorts, etc. are not found in the UK orGermany.

The estimated elasticity values for the cost of livingvariables (i.e. the CPI and RP) confirm the abovebehaviours and vary between �8.34 and �1.51. Incomparison to competing foreign countries, the elasticityvalues of the price variables vary between 0.06 and 1.23.

The magnitude of the elasticity implies that directsubstitutes for seaside tourism in Tunisia are emerging. Ifwe consider French and Italian tourists, these estimatedvalues reflect the relatively expensive services often soughtafter. In fact, being from tourist destination countries,these tourists often look for other attractions, such asSaharan (in Jerba, Zarzis and Tozeur) and cultural tourism(mainly in Tunis, Sbeitla, Tabarka and Kairouan), etc. in

relation to the typical service provided by seaside resorts(mainly in Hammamet and Sousse) (see Table 2). Conse-quently, tourism planners must take this trend intoconsideration when allocating the investment funds be-tween the different regions. Finally, the substitute pricevariable has no influence on Italian and English tourists’final choice of destination compared with the cost oftourism in Tunisia.

3.3. Error correction representation

The cointegrating residual will be denoted by z whichdesignates the extent to which the system is out ofequilibrium. It is included, as an error correction term, inthe European tourism demand model. The ECMs allow forthe short-run dynamic to converge to the long-runbehaviour of the endogenous variable (i.e. the cointegrat-ing relationship). It provides a way of combining both theshort-run (changes) and the long-run (levels) adjustmentprocess simultaneously.The ECMs are estimated using OLS method and the

results are given in Table 3. The estimated results show thatthe error correction is negative and statistically significantat a 5% level in the two equations for both Germany andthe UK while, surprisingly this is not the case for the othertwo countries. The diagnostic statistics are, however,generally satisfactory and show that the estimated ECMsare valid.

4. Forecasting

In previous studies, several econometrics models wereused to forecast tourist demand and to compare theirforecasting performances. The majority outperformed the‘no change’ model. However, few empirical studies haveadopted recent developments in econometric methodsin the areas of cointegration, ECMs and diagnosticchecking. Kulendran and Witt (2001) demonstrated thatthe forecasts produced using these methods are moreaccurate than those generated by the least square regres-sion. Song et al. (2003) showed the superiority of the naı̈ve‘no change’ model over the ECMs and their result is inagreement with Kulendran and Witt (2001) and Song andWitt (2000).Moreover, in previous studies about forecasting the

international tourist demand in Tunisia, it was demon-strated, surprisingly, that the based structural model (BSM)performed best followed by the seasonal ‘no change’ model(Ouerfelli, 2005). It is therefore relevant in this study tocompare the forecasting performances of the ECMs to thosegenerated by the BSM using forecasted statistics. Theforecast accuracies statistics were produced using Eviews5.0. and STAMP 5.0 and are presented in Table 4.The estimated values of the RMSE show that this model

is outperformed by the ECMs. These results corroboratethe idea that using seasonal non-adjusted data producesrelatively accurate forecasts.

ARTICLE IN PRESS

Table 4

The forecasting results

Countries France Germany UK Italy

Models BSM ECM BSM ECM BSM ECM BSM ECM

RMSE 0.1563 0.1112 0.1847 0.1812 0.2630 0.0784 0.2919 0.2418

Table 3

Estimated error correction models

Countries

Germany D4 lnTArr ¼ �0:014zð�1Þð�2:143Þ

þ 0:450D4 lnTArrð�1Þð4:902Þ


þ0:359D4 lnTArrð�3Þð3:404Þ

� 0:677D4 lnTArrð�4Þð�6:208Þ


� 0:349D4 lnTArrð�8Þð�3:710Þ

adj. R2¼ 0.59, DW ¼ 1.78, L–B Q(20) ¼ 17.16, J–B Norm ¼ 5.49, BG LM(2) ¼ 0.71

ARCH Test (1) ¼ 0.18

France D4 lnTArr ¼ 0:305ð5:525Þ

� 0:212D1ð�3:853Þ

� 0:354D2ð�5:026Þ

� 0:298D3ð�5:054Þ

þ 0:197z1ð�1Þð3:271Þ

þ 0:137z2ð�1Þð1:946Þ

þ 0:091z3ð�1Þð1:330Þ


� 0:445D4 lnTArrð�4Þð�4:819Þ


U. Kingdom adj. R2¼ 0.59, DW ¼ 1.75, L–B Q(20) ¼ 24.90, J–B Norm ¼ 4.00, BG LM(2) ¼ 3.29

ARCH Test (1) ¼ 0.13D4 lnTArr ¼ �0:031

ð�2:143Þ� 0:028zð�1Þ

ð�2:231Þþ 0:529D4 lnTArrð�1Þ

ð5:351Þþ 0:468D4 lnTArrð�2Þ

ð4:224Þ

� 0:680D4 lnTArrð�4Þð�5:729Þ



� 0:297D4 lnTArrð�8Þð�3:246Þ



Italy D4 lnTArr ¼ 0:104D1ð2:001Þ

þ 0:068D2ð1:276Þ

þ 0:076D3ð1:208Þ

� 0:308D4ð�0:479Þ

þ 0:096zð�1Þð1:023Þ


� 0:432D4 lnTArrð�4Þð�5:650Þ




5. Conclusion

The European demand for Tunisian tourism measuredby European tourist arrivals is modelled and forecastedusing cointegration and error correction representation.Since tourism in Tunisia is highly seasonal, it is importantto consider non-adjusted data and to model the demandusing seasonal econometric models. The seasonality cantransmit information about long run relationships betweenseries. It has been shown, using the appropriate tests, thatthis component is essentially stochastic non-stationary.This explains the usage of the quarterly data from 1981 to2005 to analyse the tourism demand from the four mostimportant European countries: Germany, France, UnitedKingdom and Italy.

The cointegration procedure and the Johansen andJuselius method are applied to estimate the long run

tourism demand elasticities which are used to comparetourists’ behaviours from different countries. The empiricalresults reveal important details concerning different aspectsin Tunisian tourism and its importance, in comparison toother destinations, in the European market.The results provide some useful insights into the effects

on income and tourism prices on European tourism demand in Tunisia. The income elasticity is used to measurethe influence of the economic conditions in the origincountry on the destination choice decision. Its estimatedvalues as well as those of the price elasticity show that thetourism in Tunisia is regarded as a luxury by tourists fromFrance and Italy, but increasingly as a necessity accordingto the tourists from Germany and the UK. The type ofproducts/services proposed (sunny beaches, dunes, oases,Spa resorts, etc.) are not found in these countries, thusinfluencing German and British tourists’ choice of Tunisiaas a destination. These important findings are useful fortourism planners in Tunisia, particularly when allocatingthe investment funds between the different regions.Furthermore, these results give an empirical justification

of the supply induced demand hypothesis. The supplyfactor is significant in the destination choice decisionparticularly for French and Italian tourists and theirdecisions are also influenced by the cost of tourism in rivalcountries.


The long run equilibrium relationships are used in errorcorrection representations to forecast the tourist arrivalsfrom each country for 1-year-ahead horizon. The rootmean squared error is used to compare the forecastingperformance of these models to those of the basicstructural model. In the short-run, the empirical findingis that the ECMs generate relatively accurate tourismforecasts. The appropriate way to use the model forforecasting would thus be through continual updating asestimates of future prices and personal income are revised.

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