Application of generalised linear regression GARMA in tourism area

摘要: From a modelling perspective, our first contribution is to propose generalised linear regression GARMA (GLRGARMA) model and generalised linear regression SARMA (GLRSARMA) model with a innovative function of explanatory variables in order to extend GLGARMA to incorporate relevant information for model fitting and forecast in tourism area. Besides, the generalised Poisson (GP) distribution is adopted to accommodate over- equal- and under-dispersion for certain tourism data. Moreover, the performance of GLRGARMA model and GLRSARMA model with their nested sub-models are compared and evaluated using several well-known selection criteria. Our second contribution is to investigate the behaviour of tourism data. The pattern of long memory is examined. The analysis of Hurst exponent, ACF plot and periodogram plot shows that Gegenbauer long memory features are presented in tourism data. Furthermore, the distinct characteristics between Gegenbauer long memory and seasonality are demonstrated to reveal the that the GLRGARMA model is more suitable for modelling tourism data. Our third contribution is to derive a Bayesian approach via the efficient and user-friendly Rstan package in estimating our proposed models. For ML approach, the likelihood function is untractable because of involving very high dimensional integrals. Several monitors of convergence of posterior samples are discussed, such as the number of effective sample and bR estimate. The criteria for modelling performance are also derived.