Denmark data.

This paper investigates the characteristics of seasonality in the tourism industry. The Gegenbauer long memory and seasonal features are clearly clarified in Denmark’s tourism data. By plotting ACF and periodogram graphs, the pattern of long memory is investigated. A generalised linear regression GARMA (GLRGARMA) model and a generalised linear regression SARMA (GLRSARMA) model with an innovative function of explanatory variables is proposed to capture data features. Furthermore, the generalised Poisson (GP) distribution with over- equal- and under-dispersion is adopted to improve model flexibility. Eight sub-models are implemented with the number of rented hotel rooms data set to explore the best-performed model structure. The Bayesian approach is adopted to implement in-sample fitting and out-of-sample forecast studies. Several model selection criteria are adopted to evaluate model performances. Overall, GLRGARMA model is the best model to handle the time series with Gegenbauer long memory feature, especially in the tourism area. The explanatory variable with the periodic sponge effect will dramatically enhance model performances.