Quantitative methods to forecasting tourist arrivals can be sub-divided into causal methods and non-causal methods. Non-causal time series methods remain popular tourism forecasting tools due to the accuracy of their forecasting ability and general ease of use. Since tourist arrivals exhibit seasonality, SARIMA models are often found to be the most accurate. However, these models assume that the time-series is linear. This paper compares the baseline seasonal Naïve and SARIMA forecasts of a seasonal tourist destination faced with a structural break in the data, with alternative non-linear methods, with the aim to determine the accuracy of the various methods. These methods include the unobserved components model, smooth transition autoregressive model (STAR) and singular spectrum analysis (SSA). The results show that the non-linear forecasts outperform the other methods. The linear methods show some superiority in short-term forecasts when there are no structural changes in the time series.