A SARIMA-ARCH Model for the Overnight-Stays Tourism in South Tyrol

Using the methodology suggested by Box and Jenkins (1970) we compare two SARIMA models for the overnight stays of the tourist in South Tyrol. We applied a seasonal unit root test suggesting that there is not seasonal unit root in the series. However, the best of the two models predicting the overnight stays considers the possibility of a seasonal unit root. Using a monthly time series of the overnight stays from January 1950 to December 2005, the best model predicting the period January 2006 to December 2008 is a SARIMA(2,1,2)(0,1,1)-ARCH(1)