Time series models are applied to outbound travel flows by air from the United Kingdom to 20 destinations. Objective assessments are made as to whether seasonal components in ARIMA processes should be modeled additively or multiplicatively. A selection strategy is presented to differentiate between the difference filters applicable to additive and multiplicative ARIMA models. The strategy inherently incorporates the possibility of increasing stochastic or deterministic seasonal variation. It is shown that neither logarithmic transformations nor a large number of difference filters are required. Selected ARIMA models tend to outperform Holt-Winters and Naïve models in terms of goodness of fit and forecasting accuracy.
Chatfield, C., and D. L. Prothero (1973). “A Reply by Dr. Chatfield and Dr. Prothero.”Journal of the Royal Statistical Society A, 136 (3): 295–315.
2.
Coshall, J. T. (2003). “The Threat of Terrorism as an Intervention on International Travel Flows.”Journal of Travel Research, 42 (1): 4–12.
3.
Divisekera, S. (2003). “A Model of Demand for International Tourism.”Annals of Tourism Research, 30 (1): 31–49.
4.
Drakatos, C. (1987). “Seasonal Concentration of Tourism in Greece.”Annals of Tourism Research, 14 (4): 582–586.
5.
du Preez, J., and S. F. Witt (2003). “Univariate Versus Multivariate Time Series Forecasting: an Application to International Tourism Demand.”International Journal of Forecasting, 19: 435–451.
6.
Franses, P. H. (1991). “Seasonality, Non-stationarity and the Forecasting of Monthly Time Series.”International Journal of Forecasting, 7: 199–208.
7.
Franses, P. H. (1998). Time Series Models for Business and Economic Forecasting. Cambridge, UK: Cambridge University Press.
8.
Franses, P. H., and A. B. Koehler (1998). “A Model Selection Strategy for Time Series with Increasing Seasonal Variation.”International Journal of Forecasting, 14: 405–414.
9.
Garcia-Ferrer, A., and A. Queralt (1997). “A Note on Forecasting Tourism Demand in Spain.”International Journal of Forecasting, 13: 539–549.
10.
Gardner, E. S. (1985). “Exponential Smoothing: The State of the Art.”Journal of Forecasting, 4: 1–28.
11.
Ghysels, E., H. S. Lee, and J. Noh (1994). “Testing for Unit Roots in Seasonal Time Series.”Journal of Econometrics, 62: 415–442.
12.
Goh, C., and R. Law (2002). “Modeling and Forecasting Tourism Demand for Arrivals with Stochastic Nonstationary Seasonality and Intervention.”Tourism Management, 23: 499–510.
13.
González, P., and P. Moral (1995). “An Analysis of International Tourism Demand in Spain.”International Journal of Forecasting, 11: 233–251.
14.
Gustavsson, P., and J. Nordström (2001). “The Impact of Seasonal Unit Roots and Vector ARMA Modeling on Forecasting Monthly Tourism Flows.”Tourism Economics, 7 (2): 117–133.
15.
Her Majesty's Stationery Office (1977–2003). Monthly Digest of Statistics. London, UK: Her Majesty's Stationery Office.
16.
Hylleberg, S., R. F. Engle, C. W. J. Granger, and B. S. Yoo (1990). “ Seasonal Integration and Cointegration.”Journal of Econometrics, 44: 215–238.
17.
Kester, J. G. C. (2002). “Preliminary Results for International Tourism in 2002: Air Transport After 11 September.”Tourism Economics, 9 (1): 95–110.
18.
Kim, J. H. (1999). “Forecasting Monthly Tourist Departures from Australia.”Tourism Economics, 5 (3): 277–291.
19.
Kim, J. H., and I. Moosa (2001). “Seasonal Behaviour of Monthly International Tourist Flows: Specification and Implications for Forecasting Models.”Tourism Economics, 7 (4): 381–396.
20.
Kim, J. H., and M. T. Ngo (2001). “Modelling and Forecasting Monthly Airline Passenger Flows Among Three Major Australian Cities.”Tourism Economics, 7 (4): 397–412.
21.
Kim, S., and H. Song (1998). “Analysis of Tourism Demand in South Korea: ACointegration and Error Correction Approach.”Tourism Analysis, 3: 25–41.
22.
Koenig, N. K., and E. E. Bischoff (2003). “Seasonality of Tourism in Wales: A Comparative Analysis.”Tourism Economics, 9 (3): 229–254.
23.
Kulendran, N., and M. L. King (1997). “Forecasting International Quarterly Tourist Flows Using Error-Correction and Time Series Models.”International Journal of Forecasting, 13: 319–327.
24.
Kulendran, N., and K. Wilson (2000). “Modelling Business Travel.”Tourism Economics, 6(1): 47–59.
25.
Kulendran, N., and S. F. Witt (2001). “Cointegration versus Least Squares Regression.”Annals of Tourism Research, 28: 291–311.
26.
Kulendran, N., and S. F. Witt (2003). “Forecasting the Demand for International Business Travel.”Journal of Travel Research, 41: 265–271.
27.
Levene, H. (1960). “Tests of Equality of Variances.” In Contributions to Probability and Statistics: Essays in Honor of Harold Hotelling, edited by I. Olkin, S. G. Ghuryel, and W. Hoeffding. Stanford, CA: Stanford University Press, pp. 278–292.
28.
Lim, C. (1997). “An Econometric Classification and Review of International Tourism Demand Models.”Tourism Economics, 3 (1): 69–81.
29.
Lim, C., and M. McAleer (2000a). “A Seasonal Analysis of Asian Tourist Arrivals to Australia.”Applied Economics, 32: 499–509.
30.
Lim, C., and M. McAleer (2000b). “Monthly Seasonal Variations: Asian Tourism to Australia.”Annals of Tourism Research, 28: 68–82.
31.
Lim, C., and M. McAleer (2002). “Time Series Forecasts of International Travel Demand for Australia.”Tourism Management, 23: 389–396.
32.
Lundtorp, S. (2001). “Measuring Tourism Seasonality.” In Seasonality in Tourism, edited by T. Baum and S. Lundtorp. Oxford, UK: Elsevier Science, 23–50.
33.
Martin, C. A., and S. F. Witt (1989). “Forecasting Tourism Demand: A Comparison of the Accuracy of Several Quantitative Methods.”International Journal of Forecasting, 5: 7–19.
34.
McKenzie, E. (1984). “General Exponential Smoothing and the Equivalent ARMA Process.”Journal of Forecasting, 3: 333–344.
35.
Osborn, D. R. (1990). “A Survey of Seasonality in UK Macroeconomic Variables.”International Journal of Forecasting, 6: 327–336.
36.
Osborn, D. R., A. P. L. Chui, J. P. Smith, and C. R. Birchenhall (1988). “ Seasonality and the Order of Integration for Consumption.”Oxford Bulletin of Economics and Statistics, 50: 361–377.
37.
Osborn, D. R., S. Heravi, and C. R. Birchenhall (1999). “Seasonal Unit Roots and Forecasts of Two-Digit European Industrial Production.”International Journal of Forecasting, 15: 27–47.
38.
Saunders, J. A., J. A. Sharp, and S. F. Witt (1987). Practical Business Forecasting. London, UK: Gower.
39.
Song, H., P. Romilly, and X. Liu (2000). “An Empirical Study of Outbound Tourism Demand in the UK.”Applied Economics, 32: 611–624.
40.
Song, H., and S. F. Witt (2000). Tourism Demand Modelling and Forecasting: Modern Econometric Approaches. Oxford, UK: Pergamon.
41.
Song, H., S. F. Witt, and T. C. Jensen (2003). “Tourism Forecasting: Accuracy of Alternative Econometric Models.”International Journal of Forecasting, 19 (1): 123–141.
42.
Song, H., and K. K. F. Wong (2003). “Tourism Demand Modelling: A Time-Varying Parameter Approach.”Journal of Travel Research, 42: 57–64.
43.
Sørensen, N. K. (1999). “Modelling the Seasonality of Hotel Nights in Denmark by County and Nationality.”Tourism Economics, 5 (1): 9–23.
44.
Turner, L. W., Y. Reisinger, and S. F. Witt (1998). “Tourism Demand Analysis Using Structural Equation Modelling.”Tourism Economics, 4 (4): 301–323.
45.
Turner, L. W., and S. F. Witt (2001a). “Forecasting Tourism Using Univariate and Multivariate Structural Time Series Models.”Tourism Economics, 7 (2): 135–147.
46.
Turner, L. W., and S. F. Witt (2001b). “Factors Influencing Demand for International Tourism: Tourism Demand Analysis Using Structural Equation Modelling, Revisited.”Tourism Economics, 7 (1): 21–38.
47.
Webber, A. G. (2001). “Exchange Rate Volatility and Cointegration in Tourism Demand.”Journal of Travel Research, 29: 398–405.
48.
Witt, S. F., H. Song, and P. Louvieris (2003). “Statistical Testing in Forecasting Model Selection.”Journal of Travel Research, 42: 151–158.
49.
Witt, S. F., and C. A. Witt (1992). Modeling and Forecasting Demand in Tourism. London, UK: Academic.
