This paper examines the degree of persistence in international monthly arrivals to Australia by using data disaggregated by tourism-source countries. We employ two competing models, which are very general in the sense that they include (seasonal and non-seasonal) unit roots as particular cases of interest. The first model is based on a long-memory process in the non-seasonal part of the series along with a short-memory autoregressive (AR) seasonal structure. The second model is based on a long-memory process for the seasonal structure of the series, the short-term evolution being described through a non-seasonal AR(1) process. Results based on the residuals and forecasting assessment indicate that the second model is preferable in terms of fitting the data. We provide persistence ranking of all countries included in the study and discuss the managerial implications of the main findings.