This study examines the persistence in the international monthly tourist arrivals to Australia by using a variety of models based on fractional integration and seasonal autoregressions. The results based on disaggregated monthly data indicate that the series are on average mean reverting, though highly persistent, and present intense seasonal patterns. A forecasting performance of several competing models was also conducted, and it was concluded that the models based on long-range dependence outperform other more standard ones based on nonseasonal and seasonal unit roots. The model based on long memory at zero and the seasonal frequencies seems to be the most accurate in this context. More detailed analysis of the results is also derived.
Adelman, I. ( 1965). "Long Cycles: Fact or Artifacts." American Economic Review, 55: 444-63.
2.
Alleyne, D. ( 2006). "Can Seasonal Unit Root Testing Improve the Forecasting Accuracy of Tourist Arrivals?" Tourism Economics, 12: 45-64.
3.
Ashley, R. ( 1998). "A New Technique for Postsample Model Selection and Validation ." Journal of Economics Dynamics and Control, 22: 647-65.
4.
Beaulieu, J.J., and J. Miron ( 1993). "Seasonal Unit Roots in Aggregate US Data." Journal of Econometrics, 54: 305-28.
5.
Bhattacharya, M., and P.K. Narayan ( 2005). "Testing for the Random Walk Hypothesis in the Case of Visitor Arrivals: Evidence for Indian Tourism." Applied Economics , 37: 1485-90.
6.
Box, G.E.P., and G.M. Jenkins ( 1976). Time Series Analysis: Forecasting and Control, 2nd edition. San Francisco: Holden-Day.
7.
Chu, F.-L. ( 2008). "A Fractional Integrated Autoregressive Moving Average Approach to Forecasting Tourism Demand." Tourism Management , 29: 79-88.
8.
Clark, T.E., and M.W. McCracken ( 2001). "Tests of Forecast Accuracy and Encompassing for Nested Models". Journal of Econometrics, 105: 85-110.
9.
Coshall, J. ( 2006). "Time Series Analysis of UK Outbound Travel by Air."Journal of Travel Research, 44: 335-47.
10.
Cuñado, J., L.A. Gil-Alana, and F. Perez de Gracia (2004). "Seasonal Fractional Integration in the Spanish Tourism Quarterly Time Series."Journal of Travel Research, 52: 408-14.
11.
Cuñado, J., L.A. Gil-Alana, and F. Perez de Gracia (2008). "Fractional Integration and Structural Breaks. Evidence from the International Monthly Arrivals in the US."Tourism Economics, 14: 13-23.
12.
Dahlhaus, R. ( 1989). "Efficient Parameter Estimation for Self-similar Process ." Annals of Statistics, 17: 1749-66.
13.
Dickey, D.A., and W.A. Fuller ( 1979). "Distribution of the Estimators for Autoregressive Time Series with a Unit Root."Journal of the American Statistical Association, 74: 427-31.
14.
Dickey, D.A., D.P. Hasza, and W.A. Fuller ( 1984). "Testing for Unit Roots in Seasonal Time Series."Journal of the American Statistical Association, 79: 355-67.
15.
Diebold, F., and L. Kilian ( 2000). "An Empirical Study of Seasonal Unit Roots in Forecasting ." Journal of Business and Economic Statistics, 18: 265-73.
16.
Diebold, F.X., and R.S. Mariano ( 1995). "Comparing Predictive Accuracy."Journal of Business, Economics and Statistics, 13: 253-63.
17.
Diebold, F.X., and G.D. Rudebusch ( 1991). "On the Power of Dickey-Fuller Test against Fractional Alternatives."Economics Letters, 35: 155-60.
18.
Gil-Alana, L.A. ( 2000). "Fractional Integration in the Purchasing Power Parity ." Economics Letters, 69: 285-88.
19.
Gil-Alana, L.A. ( 2005). "Modelling International Monthly Arrivals Using Seasonal Univariate Long-Memory Processes." Tourism Management, 26: 867-78.
20.
Gil-Alana, L.A., and J. Hualde ( 2009). "Fractional Integration and Cointegration: An Overview and an Empirical Application." In Palgrave Handbook of Econometrics , Vol. 2, Part III, Applied Econometrics , edited by T. C. Mills and K. Patterson. Basing-stoke, UK: Palgrave Macmillan, pp. 434-470.
21.
Gil-Alana, L.A., and P.M. Robinson ( 1997). "Testing of Unit Roots and Other Nonstationary Hypotheses in Macroeconomic Time Series."Journal of Econometrics, 80: 241-68.
22.
Gil-Alana, L.A., and P.M. Robinson ( 2001). "Testing of Seasonal Fractional Integration in the UK and Japanese Consumption and Income." Journal of Applied Econometrics , 16: 95-114.
23.
Goh, C., and R. Law ( 2002). "Modeling and Forecasting Tourism Demand for Arrivals with Stochastic Nonstationary Seasonality and Intervention."Tourism Management, 23: 499-510. Granger, C.W.J. (1966). "The Typical Spectral Shape of an Economic Variable."Econometrica , 37: 150-61.
24.
Gustavsson, P., and J. Nordstrom ( 2001). "The Impact of Seasonal Unit Roots and Vector ARMA Modelling on Forecasting Monthly Tourism Flows." Tourism Economics, 7: 117-33.
25.
Harvey, D.I., S.J. Leybourne, and P. Newbold ( 1997). "Testing the Equality of Prediction Mean Squared Errors ." International Journal of Forecasting, 13: 281-91.
26.
Hassler, U., and J. Wolters ( 1994). "On the Power of Unit Root Tests against Fractional Alternatives ." Economics Letters, 45: 1-5.
27.
Hoti, S., C. León, and M. McAleer ( 2006a). "International Tourism Demand and Volatility Models for the Canary Islands."Mimeo.
28.
Hoti, S., M. McAleer, and R. Shareef ( 2006b). "Modelling the Volatility in Country Risk for Tourism Economies."Mimeo.
29.
Hylleberg, S., R.F. Engle, C.W.J. Granger, and B.S. Yoo ( 1990). "Seasonal Integration and Cointegration."Journal of Econometrics, 44: 215-38.
30.
Kim, S., and K. Wong ( 2006). "Effects of News Shock on Inbound Tourist Demand Volatility in Korea." Journal of Travel Research, 44: 457-66.
31.
Kulendran, N., and S. Witt ( 2003). "Forecasting the Demand for International Business Tourism ." Journal of Travel Research, 41: 265-71.
32.
Kulendran, N., and K.K.F. Wong ( 2005). "Modeling Seasonality in Tourism Forecasting." Journal of Travel Research, 44: 163-70.
33.
Kwiatkowski, D., P.C.B. Phillips, P. Schmidt, and Y. Shin ( 1992). "Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root." Journal of Econometrics, 54: 159-78.
34.
Lee, C.K., H.J. Song, and J.W. Mjelde ( 2008). "The Forecasting of International Expo Tourism Using Quantitative and Qualitative Techniques." Tourism Management , 29: 1084-98.
35.
Lee, D., and P. Schmidt ( 1996). "On the Power of the KPSS Test of Stationarity against Fractionally Integrated Alternatives." Journal of Econometrics , 73: 285-302.
36.
Lim, C., and M. McAleer ( 2000). "A Seasonal Analysis of Asian Tourist Arrivals to Australia ." Applied Economics, 33: 1596-1619.
37.
Lim, C., and M. McAleer ( 2001a). "Cointegration Analysis of Quarterly Tourism Demand by Hong Kong and Singapore for Australia." Applied Economics , 33: 1596-1619.
38.
Lim, C., and M. McAleer ( 2001b). "Monthly Seasonal Variations: Asian Tourism to Australia ." Annals of Tourism Research, 28: 68-82.
39.
Lim, C., and M. McAleer ( 2002). "Time Series Forecasts of International Travel Demand for Australia."Tourism Management, 23: 389-96.
40.
Lim, C., and G.W. Pan ( 2002). "Inbound Tourism Developments and Patterns in China." Mathematics and Computers in Simulation, 68: 498-506.
41.
Maloney, W., and G. Montes Rojas (2005). "How Elastic Are Sea, Sand and Sun? Dynamic Panel Estimates of the Demand for Tourism."Applied Economics Letters, 12: 277-80.
42.
Narayan, P.K. ( 2005). "The Structure of Tourist Expenditure in Fiji: Evidence for Unit Root Structural Break Tests." Applied Economics, 37: 1157-61.
43.
Phillips, P.C.B., and P. Perron ( 1988). "Testing for a Unit Root in a Time Series Regression."Biometrika, 75: 335-46.
44.
Porter-Hudak, S. ( 1990). "An Application of the Seasonal Fractionally Differenced Model to the Monetary Aggregate." Journal of the American Statistical Association, 85: 338-44.
45.
Ray, B.K. ( 1993). "Long Range Forecasting of IBM Product Revenues Using a Seasonal Fractionally Differenced ARMA model." International Journal of Forecasting, 9: 255-69.
46.
Robinson, P.M. ( 1994). "Efficient Tests of Nonstationary Hypotheses." Journal of the American Statistical Association, 89: 1420-37.
47.
Rodrigues, P.M.M., and P.D.D. Gouveia ( 2004). "An Application of PAR Models for Tourism Forecasting ." Tourism Economics, 10: 281-303.
48.
Sutcliffe, A. ( 1994). "Time Series Forecasting Using Fractional Differencing."Journal of Forecasting, 13: 383-93.
49.
Turner, L.W., and S.F. Witt ( 2001). "Forecasting Tourism Using Univariate and Multivariate Structural Time Series Models."Tourism Economics, 7: 135-47.
50.
Witt, S.F., and C.A. Witt ( 1992). Modelling and Forecasting Demand in Tourism. London: London Academic Press..
