Tourism Management 25 (2004) 565–580 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.Internationaltouristarrivalswereseasonallydependableonearlierarrivalsatlaggedperiodsone,twoandfour.Thisimplies 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 visitors and tourism receipts in order to choose an appropriate strategy for its economic well-being. Hence, a reliable forecast is needed which can be done accurately via somewhat sophisticated techniques, such as Auto- regressive (Integrated) Moving Average Cause Effect (AR(I)MAX), rather than the simple cause–effect regression technique. The cause–effect regression tech- nique does not recover lagged systematical effects and unexpected changes for an accurate forecast, but, an AR(I)MAX model includes (a) autoregressive filters to account for systematical effects and (b) moving average filterstoaccountforshockeffectsinitselfinadditionto explanatory variable in the cause–effect regression model. Therefore, AR(I)MAX technique is able to outperform the simple cause–effect technique in terms of forecast accuracies. An ARMAX model includes dynamic autoregressive and moving average components in addition to theoretical explanatory variables to explain varia- tions in endogenous variables. Thus, the ARMAX model accounts for the influences other than theoretical explanations. Therefore, the ARMAX technique corrects the deficiencies of the econometric cause–effect technique by using dynamic filters to explain the variations in endogenous variables. An explanatory part is integral to the ARMA process to construct the ARMAX technique. The ARMA part is considered as a special case of ARMAX with no regressor by Greene (1990, p. 539). In other words, an ARMAX(p d q;X ) model can be explicitly repre- sented as y t ¼ m þ p 1 y t1 þ p 2 y t2 þ ? þ p p y tp þ b 0 x t þ b 1 x t1 þ ? þ b k x tk þ e t  q 1 e t1  q 2 e t2  ?  q q e tq ; ð1Þ where m is the constant term, b parameters are the regressors for lagged distributed x explanatory vari- ables, p parameters are the autoregressive parameters for lagged distributed y exogenous dependent variables, q parameters are the moving average parameters for lagged distributed e stochastic variables, and d is the ARTICLE IN PRESS *Tel.: +90-264-3460333; fax: +90-264-3460332. E-mail address: akal@sakarya.edu.tr (M. Akal). 0261-5177/$-see front matter r 2003 Elsevier Ltd. All rights reserved. doi:10.1016/j.tourman.2003.08.001