Modeling seasonality in tourism forecasting

Within the multiplicative seasonal ARIMA modeling context, there are two forecasting models, RIMA14 and ARIMA1. ARIMA14 is used for modeling stochastic nonstationary seasonality and requires first and fourth differences to achieve stationarity. ARIMA1 considers the series only in first differences, and seasonality is modeled with a constant and three seasonal dummies. The selection of either model depends on the nature of seasonality. Conventional unit root tests determine the nature of seasonality and the order of integration and, therefore, the series' choice of forecasting model. To determine whether the test correctly identifies the forecasting model for tourism demand, out-of-sample forecasting performance of ARIMA1 and ARIMA14 is compared with HEGY unit root model selection method. Comparing forecasting performance of both models with HEGY unit root model selection shows that the outcome of HEGY test procedure may not be useful in the selection of a univariate time-series model for quarterly tourism demand series.