The meaning of ARIMA models for the monthly overseas visitors is that past observations and errors have impact on the current observation. The order of 13 as suggested by the ar function applied on the osv data indicates that the monthly visitor count of the previous year also influences the visitors this month. However, it looks intriguing that the visitor count for each of the past 13 months should have an influence. Also, this increases the model complexity and we would prefer meaningful models based on as less past observations as possible. Note that the variance of the fitted models has been very large and we would like to reduce the variance too.

A good and appealing approach to integrate the seasonal impact is to use the seasonal-ARIMA model, see Chapter 10 of Cryer and Chan (2008). To understand how seasonal-ARIMA models work, we will consider the simple seasonal AR models first. Here, we allow the past few Y _t's to influence the current Y_t and then...