Forecasting Turkey's tourism revenues by ARMAX model

Tourism Management 25 (2004) 565–580

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doi:10.1016/j.tou

Forecasting Turkey’s tourism revenues by ARMAX model

Mustafa Akal*

Faculty of Economic and Administrative Sciences, Economics Department, Sakarya University, Esentepe Kampusu, Adapazarı 54187, Turkey

Received 21 December 2002; accepted 27 June 2003

Abstract

An appropriate ARMAX model is applied to forecast international tourism revenues for Turkey for the post-2001 economic

crisis. International tourist arrivals were seasonally dependable on earlier arrivals at lagged periods one, two and four. This implies

high levels of repeat visiting. Through this model, the future international tourists arrivals are forecast for the 2002–2007 period to

determine possible revenues for that same period.

International tourism revenues can be explained by the current arrivals, a first-order autoregressive and a stochastic moving

average filter at lag 3 for the 1963–2001 sample period. Future values of revenues are forecasted based on this model.

The estimated models and their forecasts may be important for the economy of Turkey which is currently recovering from the

recent economic crisis. Once US dollars expenditure per tourist is forecasted the gap between forecasts and needs can be defined

more rationally to overcome economic crises. In short, discrepancy analysis may aid marketing promotion to increase arrivals and

tourist expenditures.

r 2003 Elsevier Ltd. All rights reserved.

Keywords: International tourism; Forecasting; ARMAX; Turkey

1. Introduction

Each country wants to know its international visitorsand tourism receipts in order to choose an appropriatestrategy for its economic well-being. Hence, a reliableforecast is needed which can be done accurately viasomewhat sophisticated techniques, such as Auto-regressive (Integrated) Moving Average Cause Effect(AR(I)MAX), rather than the simple cause–effectregression technique. The cause–effect regression tech-nique does not recover lagged systematical effects andunexpected changes for an accurate forecast, but, anAR(I)MAX model includes (a) autoregressive filters toaccount for systematical effects and (b) moving averagefilters to account for shock effects in itself in addition toexplanatory variable in the cause–effect regressionmodel. Therefore, AR(I)MAX technique is able tooutperform the simple cause–effect technique in termsof forecast accuracies.An ARMAX model includes dynamic autoregressive

and moving average components in addition to

4-3460333; fax: +90-264-3460332.

ss: [email protected] (M. Akal).

front matter r 2003 Elsevier Ltd. All rights reserved.

rman.2003.08.001

theoretical explanatory variables to explain varia-tions in endogenous variables. Thus, the ARMAXmodel accounts for the influences other thantheoretical explanations. Therefore, the ARMAXtechnique corrects the deficiencies of the econometriccause–effect technique by using dynamic filters toexplain the variations in endogenous variables. Anexplanatory part is integral to the ARMA process toconstruct the ARMAX technique. The ARMA part isconsidered as a special case of ARMAX with noregressor by Greene (1990, p. 539). In other words,an ARMAX(p d q;X ) model can be explicitly repre-sented as

yt ¼ mþ p1yt�1 þ p2yt�2 þ?þ ppyt�p þ b0xt

þ b1xt�1 þ?þ bkxt�k þ et � q1et�1

� q2et�2 �?� qqet�q; ð1Þ

where m is the constant term, b parameters are theregressors for lagged distributed x explanatory vari-ables, p parameters are the autoregressive parametersfor lagged distributed y exogenous dependent variables,q parameters are the moving average parameters forlagged distributed e stochastic variables, and d is the

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max 12.200260789 16.263839665

12.20 *12.34 *12.80 *13.00 *13.26 *13.31 *13.45 *13.49 *13.74 *13.77 *14.11 *13.85 *13.95 *14.02 *14.09 *13.99 *13.91 *13.87 *13.96 *13.95 *14.23 *14.43 *14.60 *14.69 *14.88 *15.27 *15.32 *15.50 *15.53 *15.78 *15.69 *15.72 *15.86 *15.96 *16.09 *16.06 *15.83 *16.16 *16.26 *

min

Fig. 1. The time plot of LNUMR.

M. Akal / Tourism Management 25 (2004) 565–580566

degree of differencing.1 The same lag structure is notnecessarily applied to yt and et; which is required in theautoregressive distributed lag models. et is the seriallyundistributed constant variance random variable. Har-vey (1990) and Franses (1991) treat the ARMAXproblem as an extension of ARIMA modeling becausethe disturbances are generated by an ARMA(p; q)process. The first step is to ensure that the dependentvariable yt must exhibit a stationary process after theinclusion of a cause–effect relationship. In other words,yt and xt must be co-integrated to run the ARMA partof the ARMAX modeling.The stationary series is defined as exhibiting a

constant mean, a constant variance and constantautocovariances over time.2 This means exponentiallytailing down the autocorrelation function at least backtwo lags in the visual inspection based on the Box–Jenkins methodology (1970). Traditionally it can betested by various unit root tests and its econometriccause–effect part requires co-integrated series likeeconometric cause–effect techniques for a long runrelationship. There must be a significant statisticalassociation between dependent and explanatory vari-ables, as a reason for modeling and forecasting. Thestationarity of the series is inspected by the analysis ofactual autocorrelation correlogram (AC) and partialautocorrelation correlogram (PAC) in Box–Jenkinsmethodology. The existence of statistical associationbetween the dependent variable and explanatory vari-able is researched through visual inspections of the crosscorrelation function in ARMAX modeling. Errors aftercause–effect estimation should exhibit stationary non-white noise disturbances to apply ARMA part inARMAX models. Tourism receipts are theoreticallyand statistically correlated to tourist arrivals, and therest consists of lagged tourism receipts and seriallycorrelated shocks. An ARMAX model is estimatedthrough visual analysis and testing processes. It isimportant to not overparameterize among estimatedcoefficients to avoid large forecast errors.Today, tourism receipts account for 10% of the

world’s international trade. Every country wants toincrease its tourism revenues. The percentage share oftourism receipts in export earnings was 2.1% in 1963,and it was about 2.5% between 1991 and 2001 onaverage. However, the percentage share of tourismexpenditures in import expenses was 3.8% in 1963. InTurkey, from 1991 to 2001, tourism expenditures inimport expenses was on average 3%. These numbers arebelow the world’s averages, so there is a room toincrease Turkey’s tourism revenues. This is a means of

1Or an ARMAX model can be represented implicitly by lag

operators, CðLÞyt ¼ mCð1Þ þ BðLÞxt þ DðLÞet:2Or If stationary series is under the trend influence, such series is

called trend stationary.

overcoming the current account deficit and Turkishbalance of payments deficit, especially during economiccrisis.Turkey’s tourism revenues have steadily increased in

recent decades. It has increased to about US$ 7.6 billionby the year 2000 from US$ 5 billion in year 1995 andfrom US$ 0.1 billion in 1970.3 This trend is indicated byboth the time plot of the number of internationaltourists and tourism receipts as shown in Figs. 1 and 2,respectively. However, this increase is not satisfactorycompared to the majority of the world’s countries.Turkey’s world market share increased only by 0.5%from 1992 to 2000, which was 1.16% and 1.66% for thecorresponding years. On the other hand, Greeceincreased its market share of the world tourism receiptsby 0.89% from 1992 to 2000, which was 1.05% and

3See State Planning Organization (2001), International Economic

Indicators, Table 37, p. 48.

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INCT10000000

5000000 * * ** * * ** * * * ** 0 ********

0 2000000 4000000 6000000 8000000 10000000 12000000

NUMBER OF TOURIST Note:13 observations hidden

* * ** *

Fig. 2. The plot of INCT versus NUMR (US$ 1000).

M. Akal / Tourism Management 25 (2004) 565–580 567

1.94% for the respective years.4 With respect to theirtourism shares, Greece’s tourism receipts were US$ 3.3billion and Turkey’s receipts were US$ 3.6 billion in1992. Hence, one can argue that Greece has followedmore successful policies than Turkey in increasinginternational tourism revenues. However, both coun-tries, with their similar natural beauties and rich culturalheritage, received together only 2.6% of world tourismreceipts in the year 2000. The total shares of thesecountries have been below the share of one of theircompetitors, which is Italy, or France, or Spain in termsof both tourism revenues and tourist arrivals for severalyears.5

One may argue that these countries, being neighbors,may increase their world share by co-operation in thetourism sector, rather than competing with each otherbecause competition has not raised their individualreceipts to the desired level for the years. They shouldincrease the level of mass tourism through commonevents or promotions from island to islands, or region toregions, and so on, between two countries. The touroperators and hotel managers of the two countries canwork together and indeed, need to discover the benefitsof sectoral cooperation as soon as possible.

2. Literature review

Fayed and Fletcher (2002, p. 207) point out thatinternational tourism is one of the most importantsectors for the economies of countries in the world, andthey indicate that the internationalization of services isat the core of today’s economic globalization. Thus, thetourism sector also becomes an export market fordomestic goods in traditional international trade theory.Tourism revenues improve balance of payments, na-tional income and employment level of a country. Thetourism sector also provides a domestic market for some

4See State Planning Organization (2001), International Economic

Indicators, Table 38. p. 49.5For other statistics, see Ministry of Tourism (2002), Turizmde

Altin D .onem: Bir Yilin ’Icraat Raporu, p.44.

goods through tax revenues for federal and localgovernments. Moreover, this sector creates income andemployment multiplier effects in an economy. There-fore, an accurate forecast of revenues and tourists canbring economic benefits via appropriate evaluations.Erdogan (1995, pp. 83–117) considered 24 main

reasons for international traveling. Most people enjoyseeing different places as they have leisure time.Through traveling people increase their knowledgeabout the world and its cultures. It is difficult tomeasure and account for all the reasons of internationaltourist travels which are needed to set up an exactmodel. However, there are three specific determinantvariables for tourism demands modeling, namely realper capita income of tourist generating countries,exchange rate and relative prices (Sheldon, 1993). Thesevariables are generally thought to be significant inexplaining tourism demand for various countries. Inanother study on tourism demand by Uysal andCrompton (1984), real per capita income in countriesthat receive many tourists, relative exchange rates,transportation costs and promotional expenses arefound to be significant for international tourist arrivalsto Turkey. The econometric multivariate cause–effectmodels explain international tourism demands andtourism receipts with a high degree of accuracy.However the forecasts via the cause–effect econometrictechnique are not as accurate as the forecasts made viathe AR(I)MAX technique because a cause–effecteconometric model cannot adjust itself for the post-sample to explain international arrivals and tourismreceipts. But it is possible to account for such variablesimplicitly in a dynamic model by obtaining all thesystematic effects via lagged dependent and errorsystematic explanatory variables, as well as seasonality.Therefore, the effect of many influential variables forwhich we might not have data can be includedindirectly, as in the case of Turkey. In fact, Turkeydoes not have a long period of data for the variablesother than for tourist arrivals. For example, tourismadvertisement data are available only for 1990–2002.Why should one not apply an autoregressive (inte-

grated) moving average (cause–effect) (AR(I)MA(X))

ARTICLE IN PRESSM. Akal / Tourism Management 25 (2004) 565–580568

type of models as the degree of forecast accuracies ofsuch models are found to be superior to all othertechniques in a comprehensive work by Akal (2002)?These models obtain many possible systematic effectshave to be accounted for via an autoregressive and/ormoving average filter within a model. Usually, develop-ing countries do not obtain continuous data on suchvariables to account for all the effects a convenientmodel and insufficient data restrict the use of thesetechniques. In this study, an AR model is found to bemore appropriate for the yearly series of the naturallogarithmic values of the annual number of theinternational tourists and an ARMAX model isproposed for expenditure estimation in Turkey. Forthe estimation purpose, a stepwise procedure is pro-posed depending on the visual inspection of the Box–Jenkins methodology.

7And the Dickey–Fuller Unit root test (1979) with various forms

will be presented to confirm whether or not stationarity based on

3. Data and variables

All data were collected from Statistical Indicators

Yearbook, and International Economic Indicators of theState Planning Organization under The Prime Ministerof Turkey (2001). The variables used in this study aresymbolized and described as follows:

NUMRt= Yearly observed values of internationaltourist comings in Turkey, 1963–2001.

LNUMRt= Natural logarithm values of the variableNUMRt:

LNUMRt�k= LNUMR values at seasonal lags ‘‘k(1,2,4)’’.

LNUMRt4= Predicted values of LNUMRt:

INCTt= Yearly observed values of tourism revenues(1000 US dollar) of Turkey, 1963–2001.

INCTt�1= INCTt values at lag 1.INCTt

4= Predicted values of INCTt

et= Predicted values of error term; moving averagefactor.

et�3= Predicted values of error term at lag 3; movingaverage filter at lag 3.

vt= Stochastic error term used in unit root testing,white noise.

Fig. 1 represents the time plot of LUNMR series.Box–Jenkins approach requires a stationary series forthe prediction. Fig. 1 indicates a somewhat constant-stationary or a somewhat shifting constant-stationaryseries.6 However, LNUMR series is found to beanalytically stationary as a result of the analysis of theautocorrelation functions and unit root test.Forecasts of LNUMR and NUMR values are

presented for only the 2002–2007 period and these

6See Table 9 and the related footnotes 7 and 8, in addition to Fig. 3.

values are integrated with NUMR values of the sampleto forecast tourism revenues for the post-perioddepending on the pattern of the predicted model oftourism revenues, assuming the same pattern wouldcontinue during ex-post sample period.Fig. 2 indicates a positive linear relationship for

Turkey, between tourism revenues and the internationaltourists as expected. Evaluating Fig. 2 and Fig. 5simultaneously suggests a need to include the numberof tourists in the model because of that statisticalassociation.

4. Diagnostic checking and model specification

The Box–Jenkins approach is used to fit a model toboth the tourism revenues and international touristsseries. The Box–Jenkins methodology requires station-ary variables in model predictions. Since the originalinternational tourist series is found stationary butsomewhat weaker than LNUMR, based on the correlo-gram analysis,7 the NUMR values are transformed to anatural logarithm series (LUNMR). However,LNUMR indicates a somewhat stationary trend seriesin Fig. 1. But Fig. 2 clarified the issue by showing anexponentially tailing down autocorrelation function atthe back of two lags.The Ljung and Box (1978, p. 297) autocorrelation

check statistics for white noise, which are w2ð1�6Þ;6;000 ¼132:54 for LNUMR series and w2ð1�6Þ;6;000 ¼ 121:25 forthe INCT series are presented in Table 1 and Table 4,respectively.8 These numbers indicate an autocorrelatedseries and it is necessary to use an autoregressive and/ormoving average factor in the model, or anotherexplanatory variable, to have an approximately nor-mally distributed error term series, based on autocorre-lation functions. Dating back to 1963, there are nocomplete data on advertisement expenditures as animportant explanatory variable, and therefore all theeffects of other explanatory variables, including adver-tisement expenditures, can be accounted by the intro-duction of ARMA process in ARMAX models.At the beginning of model fitting to LNUMR series, a

first order autoregressive model is found to be appro-priate as a result of the simultaneous analysis of theactual, inverse and partial autocorrelation functionssimultaneously. Then, a seasonal autoregressive factorat lag 2 and then at lag 4 was necessary as a result of astepwise and simultaneous analysis of the correlationfunctions at every stage of modeling. A shift parameteror constant was found significant.

autocorrelation of the series condition holds traditionally in Section 6.8The statistics: w2 ¼ nðn þ 2Þ

Pr2k=n � k; rk ¼

Patatþk=a2t�k

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Table 1

Autocorrelation check for white noise for LNUMR

To Lag w2 DF Prob Autocorrelations

6 132.54 6 0.000 0.901 0.805 0.730 0.652 0.573 0.495

Mean of working series (LNUMR) = 14.48516 Standard deviation = 1.119081 Number of observations = 39 Autocorrelations Lag Covariance Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 0 1.252341 1.00000 | |********************| 1 1.128005 0.90072 | . |****************** | 2 1.007520 0.80451 | . |**************** | 3 0.914768 0.73045 | . |*************** | 4 0.815985 0.65157 | . |*************. | 5 0.717902 0.57325 | . |*********** . | 6 0.620270 0.49529 | . |********** . | 7 0.526051 0.42005 | . |******** . | 8 0.437718 0.34952 | . |******* . | 9 0.355806 0.28411 | . |****** . | Inverse Autocorrelations Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 1 -0.54979 | ***********| . | 2 0.11913 | . |** . | 3 -0.08708 | . **| . | 4 0.02710 | . |* . | 5 -0.01747 | . | . | 6 0.00401 | . | . | 7 0.00293 | . | . | 8 -0.00642 | . | . | 9 0.01146 | . | . | Partial Autocorrelations Lag Correlation -1 9 8 7 6 5 4 3 2 1 0 1 2 3 4 5 6 7 8 9 1 1 0.90072 | . |****************** | 2 -0.03593 | . *| . | 3 0.06441 | . |* . | 4 -0.06631 | . *| . | 5 -0.03320 | . *| . | 6 -0.05275 | . *| . | 7 -0.03526 | . *| . | 8 -0.02838 | . *| . | 9 -0.02175 | . | . |

Fig. 3. The autocorrelation functions for LNUMR.

Table 2

The autocorrelation check of residuals for AR(1)(2)(4)


6 4.19 3 0.241 0.076 �0.098 �0.033 �0.102 0.235 0.094

12 8.89 9 0.447 0.040 0.031 �0.181 �0.065 0.056 0.202

18 14.37 15 0.497 0.021 �0.058 �0.065 0.030 0.240 0.097

24 22.86 21 0.351 0.238 �0.003 �0.082 0.063 0.001 0.168


The autocorrelation check of residuals for theAR((1)(2)(4)) model is presented in Table 2. Theinsignificance level of white noise is increased above10% while w2 statistics decline to 4.19 from 132.54 forlag 1–6, and for other categorized lags. This means thatthe estimated model the ARIMA((1)(2)(4) 0 0) modelfor the LNUMR series does not require anotherautoregressive or moving average filter in the modelbecause it can be understood from Fig. 4 that no

significant spike exists. This is also implied by theautocorrelation check of residual values in Table 2.In Table 3, the correlation matrices of the estimates of

this model do not indicate over parameterization amongestimated coefficients of the lagged dependent explana-tory variables except for a constant term, which does notplay a significant role in forecast accuracy. At the sametime, the Akaike’s information criterion (AIC) andSchwartz’s Bayesian information criterion (SBC) and

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Table 3

The correlations matrices of the estimates for AR(1)(2)(4)

Parameter MU AR1,1 AR2,1 AR3,1

MU 1.000 0.652 �0.152 �0.312AR1,1 0.652 1.000 �0.249 �0.431AR2,1 �0.152 �0.249 1.000 �0.252AR3,1 �0.312 �0.431 �0.252 1.000

Fig. 4. The autocorrelation functions of residuals for LNUMR: AR(1)(2)(4).


mean square error criterion (MSE) are given attention inminimizing their values in the modeling.Similar to Table 1 for the LNUMR series, Table 4

also indicates an autocorrelated INCT series. However,an ARMAX model is preferred instead of an ARIMAmodel to fit the INCT series because tourism revenuesare meaningfully correlated to the number of interna-tional tourists. The other reason is that Akal (2002)found AR(I)MAX technique to be more applicable interms of forecast accuracy as a result of comparisonaccuracy performances of various techniques.In the estimation of the ARMAX (1 0 3, NUMR)No

Intercept model for tourism revenues, the cross correla-tion function between the INCT and the NUMRvariable is examined to define the degree of lag. This isshown in Fig. 5. As a result, the highest correlation

between INCT and NUMR existed in the current year.This is used as the input variable for the model.Furthermore, a long run relationship seems to exist

between international tourism revenues and touristarrivals because the cross correlation function indicatesconstantly decreasing significant spikes at further lags.Table 5 shows the maximum likelihood estimation of

the cause–effect part of the ARMAX model. Table 6shows the autocorrelation check of residuals of thismodel. The autocorrelation check statistics for whitenoise indicated the need for the inclusion of anautoregressive or moving average factor, or both.However, one needs to minimize AIC and SBC furtherby defining orders of AR and MA filters. At the sametime, the corresponding correlograms of the estimatedresiduals shown in Fig. 6 indicate the necessity for animprovement of the model. Furthermore, the plot of theresiduals of this model are stationary except for inverseautocorrelation function, as seen in Fig. 6, to fitAR(I)MA part.Examination of these autocorrelation functions in-

dicated a first-order autoregressive factor at lag 1, then,after this factor was included in the model, a movingaverage factor at lag 3 is then included to increase thesignificance of white noise. As a result, w2 statisticsdecline to 3.27 from 91.85 (Table 6) in the simple

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Table 4

Autocorrelation check of white noise for INCT


6 121.25 6 0.000 0.864 0.763 0.733 0.637 0.529 0.433

Fig. 5. The cross correlation function of INCT and NUMR.

Table 5

Results of maximum likelihood estimation of ARMAX(0-0-

0,NUMR)No Intercept

Parameter Estimate Std Error T Ratio Lag Variable

NUM1 0.66811 0.01815 36.81 0 NUMR

Variance Est.=2.94201E11, Std Error Estimate=542403.292, AIC=

1141.55784, SBC=1143.2214, N ¼ 39; wð1Þ;0:118 ¼ 2:441; DW ¼ 0:272;R2E0:97:


econometric model with NUMR and 121.25 (Table 4) ofthe original auto correlated INCT series. The prob-ability level of white noise improved to 0.514 in lag 1 tolag 6, 0.609 in lag 1–12, to 0.818 in lag 1–18 and to 0.958in lag 1–24 in ‘‘ARMAX (1 0 3, NUMR)No Intercept’’as seen in Table 7.Fig. 7 indicates that nothing is left significant in

the model because the distribution of residuals isa white noise process. Additionally, the inverse auto-correlation function is stationary. Therefore, the‘‘ARMAX(1 0 3,NUMR)No Intercept’’ seems the mostconvenient model to explain and thus forecast interna-tional tourism revenues.Similar to diagnostic checking of the LNUMR model,

the correlations matrices of the estimates of the‘‘ARMAX(1 0 3,NUMR)No Intercept’’ model forINCT does not indicate overparameterization among

the coefficients of explanatory variables, shown inTable 8. However, if there were overparameterizationamong estimated coefficients of the exogenous variables,the forecast error would be higher because one of thehighly correlated parameters can manage and directforecasts against forecast accuracy (Akal, 2002).By choosing the first-order autoregressive and a

moving average filter at lag 3, the AIC, SBC and MSEcriteria related to estimated errors are minimized.

5. Unit root and co-integration tests for the variables

In addition to the visual inspection or correlogramanalysis used above, one may need to test traditionallywhether a unit root problem exists in the series. TheDickey–Fuller unit root test is run in each LNUMR,INCT and NUMR to test their stationarities. The nullhypothesis of non-stationarity (exhibiting unit rootprocess) is tested against the alternative hypothesis ofstationarity (exhibiting no unit root process). For theco-integration test, the null hypothesis is set as ‘‘seriesare not co-integrated’’ and tested against ‘‘co-integra-tion’’ under an alternative hypothesis. If the nullhypothesis is accepted, the series will be non-co-integrated. For the testing purpose, the calculatedDickey–Fuller ‘‘t’’ statistics, referring to the coefficientof lag 1 levels, were evaluated at critical Dickey–Fuller

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Table 6

Autocorrelation check of residuals for ARMAX(0 0 0,NUMR)No Intercept


6 91.85 6 0.000 0.802 0.680 0.667 0.545 0.404 0.282

12 110.77 12 0.000 0.267 0.256 0.184 0.206 0.274 0.245

18 127.69 18 0.000 0.257 0.234 0.221 0.225 0.144 0.118

24 129.76 24 0.000 0.110 0.068 0.029 �0.005 �0.039 �0.068

Fig. 6. The autocorrelation functions of residuals for ARMAX(0-0-0,NUMR)No Intercept.

Table 7

The autocorrelation check of residuals for ARMAX(1 0 3,NUMR)No Intercept


6 3.27 4 0.514 �0.018 �0.020 �0.094 0.230 0.069 �0.06512 8.20 10 0.609 0.009 0.154 0.082 �0.080 0.146 �0.17318 10.87 16 0.818 0.089 �0.044 0.122 0.123 �0.016 �0.00024 11.99 22 0.958 0.061 0.049 �0.010 0.052 �0.025 0.053

9Referring the test by Brierens (‘‘Testing Stationarity’’ for US

inflation rate, 1961–1987), for which stationarity was the null did not

reject the null of stationarity even correlogram tapered off, applying

Phillips–Perron parametric unit root test.


‘‘t’’ values. However, one must be aware that if unit roottests and the Box–Jenkins approach give conflictingresults, it is important to examine why this is so. Itsometimes happens that a unit root test does not rejectthe null hypothesis of unit root (at the traditionalsignificance levels), although the correlogram tapers off.Hence it is important to examine the correlograms

before applying any unit root tests (Maddala, 1992,p. 585).9 In Table 9, some regressions are estimated and

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Fig. 7. The autocorrelation functions of residuals for ARMAX(1 0 3,NUMR)No Intercept.

Table 8

The correlations matrices of the estimates for ARMAX(1 0 3,

NUMR)No Intercept

Variable Parameter MA1,1 AR1,1 NUM1

INCT MA1,1 1.000 0.273 0.292

INCT AR1,1 0.273 1.000 0.424

NUMR NUM1 0.292 0.424 1.000

10Therefore, the unit root regression might not be enough to

conclude for non-co-integration unless autoregressive factors are

allowed to reach errors in the white noise process.11w2(1�6), 6,.482 =5.5 for DNUMRt series.


compared with each other for a conclusion in additionto visual analysis. Since these models exhibited insignif-icant coefficients compared to Dickey–Fuller criticalvalues, the decisions were in favor of no unit root for allthe variables. On the other hand, correlogram analysisof each LNUMR, NUMR and INCT series indicated astationary series which is consistent with the unit roottest results in Table 9. All the alternative estimatedmodels indicated white noise in errors. Since theinclusion of autoregressive factors, constants or trendsin the unit root regressions made the coefficient of thelagged factor at the level of a variable and theconsequent regression insignificant, one cannot acceptthe unit root process stated by the null hypothesis. Sinceone is not interested in insignificant coefficients in thetest we can eliminate such variables in the models. As aresult, the regressions with a significant coefficient at lag

1 of the levels of the LNUMR, NUMR, and INCTshowed that the whole series was stationary andappropriate in regards to the Box–Jenkins methodology;in other words, the decisions based on the visualinspections are validated by the Dickey–Fuller test.Since the LNUMR series is better than the originalNUMR, the LNUMR series is used to fit a model andits forecasts are used in forecasting tourism revenues asan input variable.However, the predicted errors series of the simple

econometric cause–effect model of the levels is found tobe stationary but not exhibiting a white noise in errorsbased on the correlogram analysis.10 This is looked forin an ARMAX model. On the other hand, thecorrelograms of the first differences of all seriesindicated white noise process.11 But, this is not soughtin an AR or MA processing. The stages of ARMAXtype models start with non-white noise but with thestationary series, and finish with a white noise. This isachieved by visual analysis. Therefore, the INCT andNUMR series are convenient for such modeling. On theother hand, the correlograms of the estimated residuals

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Table 9

Unit root test results for the variables

Dependent variable t-statistics C.V.( %1,%5,%10)� Decision

DLNUMRa 4.10 (�2.64,�1.95,�1.61) No unit root (stationary)

DLNUMRb �1.46 (�3.65,�2.97,�2.61) Insignificant model

DINCTc 5.52 (�2.64,�1.95,�1.61) No unit root (stationary)

DINCTd 1.06 (�3.65,�2.97,�2.61) Insignificant model

DNUMRe 2.76 (�2.64,�1.95,�1.61) No unit root (stationary)

DNUMRf �1.01 (�4.26,�3.54,�3.21) Insignificant model

Detg �2.14 (�2.64,�1.95,�1.61) Co-integrated (stationary)

De1;th �6.50 (�2.64,�1.95,�1.61) Co-integrated (stationary)

De2;ti �6.12 (�2.64,�1.95,�1.61) Co-integrated (stationary)

(1) For DINCTt=0.79033 DNUMR t+et simple regression model, where et estimated error term.

(2) No constant, no trend, no AR for the residuals of ARMAX(1 0 3,NUMR)No Intercept model. There is no AR factor because et exhibited a

white noise, and thus, both constant and trend coefficients are found insignificant.

(�) The critical values are given by Maddala (1992), Introduction to Econometrics, p. 606, and Enders (1995), Applied Econometric Time Series,p. 419, depending on W.A. Fuller (1976), Introduction to Statistical Time Series, p. 371.

gFor Det¼ �0:26288et�1þ0:99997Det�3 þ vt; where vt is w.n., and et¼ INCTt�0:66811 NUMRt. However, autocorrelation functions of the

residuals of this model indicated stationary series based on correlogram analysis.hFor Det¼ �1:10271et�1 þ vt; where vt is w.n., and et¼ DINCTt�0:79033DNUMRt: The only significant correlation between INCT and NUMR is

about 0.90736 at lag zero. That is the indication of the short run relation between the INCT and NUMR series.iFor Det¼ �1:01296et�1 þ vt; stationary, where vt is w.n. And et belongs to the ARMAX model. The equation with constant is estimated as

follows:

, where vt is w.n.


ARTICLE IN PRESS

Table 10

Maximum likelihood estimation for LNUMR

Parameter Estimate Std error T ratio Lag

MU 13.97587 2.68139 5.21 0

AR1,1 0.98637 0.03946 25.00 1

AR2,1 0.34255 0.16464 2.08 2

AR3,1 0.40408 0.19798 2.04 4

Constant Estimate=0.07462306, Variance Estimate=0.0266091, Std

Error Estimate=0.16312295, AIC=�20.435516, SBC=�13.781269,Number of Residuals=39, Estimated Mean=13.9758688, Autoregres-

sive Factors: (1–0.98637 B��(1))(1–0.34255 B��(2))(1–0.40408 B��(4)).


of the model, based only on the first differences, did notrequire an inclusion of AR and/or MA factor to run anARIMAX model.The co-integration test for the ‘‘ARMAX(1 0 3,

NUMR)No Intercept’’ model indicated co-integratedINCT and NUMR series because the estimated t isfound to be greater than the critical values. Thus, thereexists a long run as well as a short run relationship asindicated by the crosscorrelation functions.12 The crosscorrelation function between INCT and NUMR in-dicated a long run relationship. These results imply nospurious regression.13 There is also a short run relation-ship because the cross correlation function betweenINCT and NUMR indicated a significant spike at lagzero. The plot of the autocorrelation functions of theresiduals of ARMAX model indicated the white noiseerror series.14

6. Results and interpretation

The implications of the estimated models for thetourism sector and the economy of Turkey will now bediscussed. For this, one needs to explicitly explain theeffect an earlier visit could have on today’s internationaltourists arrivals in the country to further develop thetourism sector. The higher the quality of services andhospitality, the higher the number of tourists and thusthe higher the international tourism receipts, and so thelarger the market and the better the economy.The following models were found to be the most

convenient after the visual diagnostic checking, analy-tical unit root and co-integration tests.

6.1. The estimated model for the international tourists

Table 10 shows a significantly estimated AR((1)(2)(4)) model. According to the statistics in thistable, the natural logarithmic form of the internationaltourists is found seasonally dependable on lags 1, 2 and4. According to this model, the most effective determi-nant of current visits is the previous year’s tourist

12Both the fist differences of INCT and NUMR indicated a

significant cross correlation spike only at lag zero, which is not shown

here but one may guess it from the constant increases or decreases of

cross correlation function of INCT and NUMR (Fig. 5).13And the cross correlation function between INCT and time, and

between NUMR and time did show similar significance in decaying

spikes at lags away from the current level.14However, allowing autoregressive factors in the co-integration test

equation yields insignificant AR and coefficient of et�1 compared to

the Dickey–Fuller critical values. This result would mean non-co-

integration between the series. Similar results were seen in unit root

tests of individual series above when the regressions are run with a

constant term, and constant with trend, and autoregressive factors,

etc., whether some of their coefficients are significant or not in a model.

These models were found to be insignificant.

arrivals among the lagged effects, as seen in equationtwo, which illustrates explicitly the results of Table 10.The original forecast values of the number of interna-tional tourists are used to forecast international tourismrevenues because the revenue model regressed on theuntransformed values of the international tourists. Infact, the expansion of Table 10 resulted in the followingequation:

ð2Þ

w2ð1�6Þ ¼ 4:19; w2ð6�12Þ ¼ 8:89; w2ð12�18Þ ¼ 14:37;

w2ð18�24Þ ¼ 22:86; AIC ¼� 20:44; SBC ¼� 13:78;

rAR1;MU ¼ 0:652; rAR2;MU ¼ �0:152;

rAR3;MU ¼ �0:312; rAR1;AR2 ¼ �0:249;

rAR3;AR2 ¼ �0:252; R2 ¼ 0:91513; F ¼ 125:8:

Therefore, the current year’s international touristvisits are linked back to over seven years of arrivals.However, the current arrivals are affected negatively bythe values of lags at 3, 5 and 6 as a result of iteration ofthe seasonal (AR(1)(2)(4)) model. These negative effectsare covered up by the positive effect of the lag 1, 2, 3 and7. The variations in international tourist arrivals can beexplained about 91.5% by earlier arrivals.15

6.2. The estimated model for the tourism revenues

The following model is found appropriate for inter-national tourism receipts. This model indicates that thecurrent years’ tourism revenues can be explained

15The author also considers the advertisement expenditures as an

important variable for tourist arrival but the advertisement expendi-

tures are only available after 1990, which is a very short time period for

econometric modeling.

ARTICLE IN PRESS

Table 11

Maximum likelihood estimation for INCT

Parameter Estimate Std Error T Ratio Lag

MA1,1 �0.65739 0.14975 �4.39 3

AR1,1 0.77262 0.11064 6.98 1

NUM1 0.72044 0.03961 18.19 0

Variance Estimate=6.50984E10, Std Error Estimate=255143.92,

AIC=1087.75906, SBC=1092.74975.

Number of Residuals=39, No mean term in this model, Autoregressive

Factors: 1–0.77262 B��(1),Moving Average Factor: 1+0.65739 B��(3),Overall Regression Factor: 0.72044.

16The estimated of the simple econometric-cause effect model at the

levels yielded a MAPE about 52% for the 1995–2001 period, which is

not presented here.


regarding 99.375% of the current number of tourists,the previous year’s tourism receipts and by a systematicerror term at lag 3. Table 11 shows that all coefficientsare significant at po0:01: The estimated model issignificant and does not indicate a structural change.As a result of the Chow Prediction Test, the tourismreceipts, with respect to the tourist arrivals is stable forthe entire period. The test is established based on thequestion of whether Turkey’s tourism polices mighthave caused a change in the effect of the tourist arrivalson the revenues after 1980 compared with the 1963–1980period. The Null hypothesis of ‘‘no structural change’’ isaccepted. This implies that the distribution of touristarrivals by blocks or by countries is stable for theperiod, and it is assumed to be stable for the out-offsample period for forecasting. The revenue model, likethe tourist arrival model, does not indicate overpar-ameterization among estimated coefficients. This isdesirable so as not to cause large forecast errors.The model can be presented as follows:

ð3Þ

w2ð1�6Þ ¼ 3:27; w2ð6�12Þ ¼ 8:20;

w2ð12�18Þ ¼ 10:87; w2ð18�24Þ ¼ 11:99;

AIC ¼ 1087:7; SBC ¼ 1092:7;

rNUM;AR ¼ 0:424; rNUMMA ¼ 0:424;

rAR;MA ¼ 0:273; R2 ¼ 0:99375; F ¼ 1908:

Chow Structural F1963�1979; 1980�2001 ¼ 1:75149;

Goldfeld-Quandt F1963�1977; 1987�2001 ¼ 1:10481:

According to equation three, each additional touristtends to spend about US$ 720 and this increases therevenues of the next year by about US$ 773 on average,Ceteris paribus. Each tourist adds to Turkey’s revenuesand, in the long run, each additional tourist tends tospend approximately US$ 3168 on average in the longrun. This also means that each tourist has a flow effecton the international tourism revenues. The coefficient ofthe moving average order at lag 3 is found to be negativeand thus its effect on revenue receipts is positive because

of the structure of ARMA model, which may beinterpreted as a positive shock by lag 3 to the model.In addition, one can see that tourism of the current

year has revenues that depend on NUMRt�3, INCTt�4,

et�6; etc., if the et�3 term is replaced by the actual andforecasted values, ‘‘INCTt�3�INCT

4t�3’’.

Estimated short run international tourist elasticity ofrevenues is about 0.976. This result was also indicatedby the estimated first-order differencing model which is

ð4Þ

w2ð1�6Þ;259 ¼ 7:72; w2ð6�12Þ;0:151 ¼ 16:98;

w2ð12�18Þ;401 ¼ 18:85; w2ð18�24Þ;67 ¼ 20:46;

AIC ¼ 1059:2; SBC ¼ 1060:9; DW ¼ 2:15;

R2 ¼ 0:8445; F ¼ 200:9:

Based on this model, the short run internationaltourist elasticity of tourism revenues is estimated about0.96129% which is very close to the 0.976% of ARMAXmodel, although there is missing information as a resultof the first differences, but not having a serial correla-tion process at the first-order differences.The long run international tourist elasticity of

revenues is about 3.09%. These results imply that 1%increase in the number of international tourists wouldincrease the revenues by 0.96% in the short run and by3.09% in the long run on the average. That is to say thatthe international tourism revenues of Turkey is lesselastic in the short run and elastic in the long run withrespect to international tourists comings in the country.On the other hand, the estimated first differences

model did not necessitate inclusion of an autoregressiveand/or moving average filter to run an ARIMAX modelso one might be able to improve forecast accuracyfurther.

6.3. The forecast values of international tourists and

tourism revenues and evaluation

Table 12 shows the out of sample forecast values ofthe natural logarithm of the international tourists series.These are reliable at 5% significance level.Table 14 shows the out of sample forecasts of

revenues and their reliability at a 5% significance levelbased on the ARMAX model. These values are alsoreliable. Since simple cause–effect econometric modelsdo not show good performance in forecasting the futurevalues of revenues are forecasted by ARMAX model.16

The third equation resulted in mean absolute percentageerror (MAPE) of around only 3% as seen in Table 13.

ARTICLE IN PRESS

Table 12

Forecasts intervals for variable LNUMR

Year Forecast Std error Lower 95% Upper 95%

2002 16.3371 0.1631 16.0174 16.6569

2003 16.2477 0.2291 15.7987 16.6968

2004 16.3962 0.3139 15.7809 17.0115

2005 16.4263 0.3786 15.6842 17.1683

2006 16.4474 0.4793 15.5080 17.3867

2007 16.3935 0.5601 15.2957 17.4912

Table 13

Mean absolute percentage error accuracy criterion of the estimated

Models

Year MAPE� MAPE�� MAPE�� MAPE��

1995 16.5412 4.46188 3.97928 0.64317

1996 9.5066 3.89634 4.71104 0.89420

1997 10.3778 5.06618 3.99109 0.66939

1998 8.4283 6.85068 5.16112 1.73201

1999 14.6474 6.25706 4.35623 3.07960

2000 16.6816 6.69733 4.56233 3.20215

2001 16.4707 7.61965 4.47203 3.11247

�For estimated LNUMR model, calculated over anti-natural loga-

rithms of estimated LNUMR values.��For INCT4

t ¼ 0:668107 NUMRt,�� DINCT4

t ¼ 0:79033 DNUMRt.��For INCTt

^=0.720439 NUMRt+0.77262 INCTt�1þ0:65739et�3:

Table 14

Forecasts intervals for variable INCT

Obs Forecast Std Error Lower 95% Upper 95%

2002 9115637.44 255143.9 8615564.54 9615710.33

2003 8506632.06 322425.4 7874689.84 9138574.28

2004 9900625.99 356588.0 9201726.31 10599526

2005 10103063 456738.6 9207871.92 10998254

2006 10244369 507182.2 9250310.06 11238428

2007 9666360.73 535031.9 8617717.44 10715004

Table 15

Forecast values of tourists and tourism revenues

Year Number Revenues (US$ 1000)

2002 12448832.07 9115637.44

2003 11384092.01 8506632.06

2004 13206237.99 9900625.99

2005 13609165.22 10103063.11

2006 13899513.62 10244368.98

2007 13170001.28 9666360.73


By using ARMAX model, MAPE is calculated as0.643% for 1995 and 3.112% for 1995–2001. Further-more, the forecasted tourism revenues based on theARMAX models should not be expected to have aMAPE of more than 3% for 2002–2007 period becausethe shorter the forecast period is the smaller the forecasterror. There are accuracy gains of between 1% and 5%in passing from the simple models of the ARMAXmodel of tourism receipts, as Table 13 indicates.Regressing tourist arrivals on did other variables wasfound not to cause a significant change in the values ofthe revenue forecasts and in the MAPE.Governmental and private advertisement expendi-

tures can also influence people’s decisions. Unfortu-nately, Turkey does not have an advertisementexpenditures archive for the period before 1990. Hence,

it is not included in the tourist arrivals models and isassumed to be defined exogenously in the revenuesmodel. Indeed, inclusion of too many variables in amultivariate model causes over parameterization, andthus larger forecast errors (Akal, 2002).However, inspection of forecasts in Table 15, in-

dicates that these numbers will not be sufficient topermit Turkey to recover from current economic crisis.Thus, today’s tourism industry must be developedfurther to reach the governmental target of abouttwenty million international tourists in the year 2010.Sensilay (2001) points out that the international

tourism of Turkey in 2001 was ‘‘ordinary’’ because itwas, as expected, based on extensions of the earliertrend. In fact, he argued that the things which were donein these years were inappropriate for the TurkishTourism sector if the forecasts above were to be takenas a criterion for various policies or strategies such as (i)extending tourism to whole year, (ii) opening newtourist areas, (iii) promoting foreign direct investmentin the sector, (iv) supporting tourism depending onhistory, culture and religion in all of Anatolia, (v)investing in services that match the expectations of thethird generation, (vi) opening recreational areas in theAnatolia, and more importantly and (vii) cooperatingand coordinating with Greek tourist organizations bypromoting joint country journeys as two neighboringcountries that both shared an important role in theancient world. In other words, both countries shouldminimize frontier controls. The following sentences areof importance ‘‘During Alexandra the Great in 334 B.C.some 700,000 tourists would crowd in Ephesus (in whatis now Turkey) in a single season to be entertained bythe acrobats, animal acts, jugglers, magicians, andprostitutes who filled the streets. Ephesus also becamean important trading center and, under Alexander, wasone of the most important cities in the ancient world’’(McIntosh, Goeldner, & Ritchie, 1995). In short, thenumber of international tourists at the beginning of thetwenty-first century seems lower than in Ephesus in 334B.C., in terms of population and transportation facil-ities. These numbers illustrate the necessity for coopera-tion and coordination of Turkey with Greece to increasetheir share in the world’s ‘‘peace industry’’.

ARTICLE IN PRESS

Table 16

Averages of Per Tourist Receipts of Turkey (US$)

Period N Mean Std Dev Minimum Maximum Growth (%)

1963–2001 39 363.5091967 262.4883280 23.0274103 769.2972599 11.29

1963–1969 7 36.5724735 9.5027346 23.0274103 52.6814639 5.32

1970–1979 10 148.9891584 57.7529716 67.8787368 254.7485111 15.22

1980–1989 10 458.0260914 141.5193908 272.8658790 676.6452822 6.96

1990–2001 12 654.2249048 93.1620381 477.9430369 769.2972599 2.32

Source: Calculated from data.


7. Market structure and operation

From Table 16, Turkey’s tourism receipts per touristhas increased significantly since 1963.17 This is the resultof new facilities that began to be established by the1980s. Also, new market strategies such as establishingmass tourism facilities, increasing the quality of tourismservices, targeting richer tourists in the richer westerncountries, like European Union countries and America,etc., by advertisements, have attracted internationaltourists and increased receipts.Governments and other agents in the tourism sector

know that the per tourist receipts could be raised byattracting richer tourists. However, one may estimateeach country’s tourism spending tendency if there arecomplete data for countries. But, in this time seriesstudy, it is assumed that they have similar spendingtendencies. Moreover, Goldfeld-Quandt test statisticswith ‘‘F13;13 ¼ 1:10481’’ indicate the acceptance of ‘‘noheteroscedasticity’’ under Null Hypothesis at 5%significance level. And the models estimated aboveindicated the existence of long run relationship betweentourism receipts and the tourist arrivals. The ChowPrediction Test statistics with ‘‘F ¼ 1:75149’’ indicatesthat the estimated regressor of the tourism receipts withrespect to the tourist arrivals is stable for the entireperiod. This concurs with the volume of tourist arrivalsby countries over time, as shown in Tables 17 and 18.This would also imply that the average tourist spendingof the countries is statistically stable for the period.Table 17 indicates that the European Union ranks firstand 64% of international tourists come from OECDcountries, which mostly have high per-capita income.The distribution of tourist arrivals by countries is

shown in Table 18 for the years of 1999–2001. Germanyranks first, and the United Kingdom ranks second in theperiod. The other European countries and Americafollow them.With cooperation and coordination by Turkey with

Greece, rather than competition, tourism operators andhotel managers in the two countries would capitalize on

17For yearly average expenditures, see http://turizm.gov.tr/statistics/

Balance of Tourism Receipts-Expenditure Per Person.

the desires of tourists to see both countries which sharesimilar ancient cultural values in a similar manner.

8. Conclusion

Ninety-one percent of the variations in internationaltourist arrivals can be explained by earlier arrivals. Theestimated ARMAX model indicates that the currentyears’ tourism revenues can be explained regarding99.4% of the current number of tourists, the previousyear’s tourism receipts and by a positive systematic errorterm at lag three. The estimated international touristselasticities of the tourism receipts imply that 1%increase in the number of international tourists wouldincrease the revenues by 0.96% in the short run and by3.09% in the long run on the average.Assuming the pattern indicated by the estimated

models above is valid for the post-sample period, 2002–2007, tourism revenues are expected to be about US$9,115,637,440 as a result of 12,448,832 internationaltourists forecasted for the year 2002. These numbersdiffer from the governmental targets, which are above13 million tourists and US$ 11–12 billion revenues. Thereason could be due to policy choice. For example,recently, Turkey started to spend much more moneythan it used to spend for advertising. Even if thegovernments reach their targets, the current revenues arenot enough to overcome a crisis projected for the year2002. Therefore, it is necessary to develop alternativepolicies, tourism facilities and new advertisementstrategies to further increase revenues, and thus theefficiency in the market.The success of the Turkish soccer team in the World

Cup of 2002 might help reduce the currency gap becauseit was considered an excellent advertisement for Turkishtourism. Joint tournaments between Greek and Turkishoperators may also help Turkey’s economy. But, sinceThe Second Gulf War will reduce world trade demandas well as tourism demand for all countries, includingTurkey and Greece. This necessitates cooperationbetween the two neighbors in tourism sector.On the other side, policies may change the pattern of

these models and thus the forecasted values. However,

http://turizm.gov.tr/statistics/

ARTICLE IN PRESS

Table 17

Distribution of tourist arrivals by blocks

%2000 Blocks 1984 1990 1995 2000

53.23 Europe Union 847,397 2,734,640 3,794,034 5,551,056

56.65 Europe OECD 986,989 3,331,519 4,001,017 5,907,730

64.07 Total OECD 1,260,632 3,663,427 4,464,222 6,681,384

13.26 U.I.S 15302 223,211 1356735 1383110

2.74 Yugoslavia 179705 325703 70034 285930

23.23 East Europe Tot. 277,846 1,014,600 2,022,249 2,422,962

1.61 Total Africa 92,632 89,924 135,816 167,829

5.97 T. West Asia 289,104 620,562 622,187 270,992

4.60 Tot. South Asia 200,240 301,718 431,617 480,022

10.57 Total Asia 471,232 590,822 1,052,179 1,102,209

0.02 Oth. North America 362 2560 3786 2455

0.05 Oth. Cent. America 883 3548 3819 5270

0.03 Oth. South America 4433 12,055 3434 7725

0.33 Tot. South America 12,508 20,760 35,628 34,318

0.40 Total America 13,753 26,868 43,233 42,043

0.01 Oceania 40 2 464 842

0.10 Haymatlos 959 3665 8723 10,884

100 Total Foreign 2,117,094 5,389,308 7,726,886 10,428,153

Source: Ministry of Tourism (2002), http://turizm.gov.tr/statistics/Distribution of Foreigners Arriving in Turkey by Nationalities.

Table 18

Distribution of tourist arrivals by most visiting countries

Rank Countries 2001 (%) 2000 (%) 1999 (%)

1 Germany 24.82 21.84 18.55

2 UK 7.28 8.78 10.88

3 Russia 6.52 6.49 5.86

4 Netherlands 5.45 4.22 2.86

5 Bulgaria 4.65 3.66 3.46

6 France 4.51 4.31 3.61

7 USA 3.70 4.94 5.28

8 Austria 3.10 3.07 1.73

9 Iran 2.82 3.65 4.70

10 Italy 2.71 2.10 1.06

11 Israel 2.67 2.99 2.69

12 Belgium 2.67 2.46 2.00

13 Sweden 1.73 1.42 1.43

14 Greece 1.70 2.10 1.96

15 Romania 1.56 2.54 6.45

16 Other 24.12 25.41 27.48

Total 100 100 100

Source: Ministry of Tourism (2002), Turizmde Altın D .onem: Bir Yılın’Icraat Raporu, p. 27.


an AR(I)MAX type model may overcome the effects ofsuch policies better than other types of models, such asthe econometric cause–effect models that used to beapplied to explain tourism demand in tourism literature.Therefore, on average, AR(I)MAX models would out-perform econometric cause–effect and trend models interms of forecast accuracy by accounting for the effectsof the political and economic instabilities throughautoregressive and moving average filters, because theAR(I)MAX technique is based on a stationary dynamicprocess and co-integrated series. It must also be notedthat, the estimated ARMAX technique outperformed

the simple econometric cause–effect technique in termsof accuracy. By using ARMAX model, MAPE iscalculated as 0.643% for 1995 and 3.112% for 1995–2001, which are much lower than the econometric-causeeffect model’s estimation. Finally, according to revenuemodel, each additional tourist tends to spend about US$720 and this increases the revenues of the next year byabout US$ 773 on average, ceteris paribus. Also, it wascalculated that each additional tourist adds to Turkey’stourism revenues approximately US$ 3168 on theaverage in the long run.

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Forecasting Turkey's tourism revenues by ARMAX model