Forecasting of Tourist Arrivals Using Subset, Multiplicative or Additive Seasonal ARIMA Model

Abstract

Most of Seasonal Autoregressive Integrated Moving Average (SARIMA) models that used for forecasting seasonal time series are multiplicative SARIMA models. These models assume that there is a significant parameter as a result of multiplication between non-seasonal and seasonal parameters without testing by certain statistical test. Moreover, most popular statistical software such as MINITAB and SPSS only has facility to fit multiplicative models. The aim of this research is to propose a new procedure for indentifying the most appropriate order of SARIMA model whether it involves subset, multiplicative or additive order. In particular, the study examined whether a multiplicative parameter existed in the SARIMA model. Data about the number of tourist arrivals to Bali, Indonesia, were used as a case study. The model identification step to determine the order of ARIMA model was done by using MINITAB program, and the model estimation step used SAS program to test whether the model consisted of subset, multiplicative or additive order. Modeling of the data yielded an additive SARIMA model is the best model for forecasting the number of tourist arrivals to Bali. The comparison evaluation showed that additive SARIMA model yielded more accurate forecasted values at out-sample datasets than multiplicative SARIMA model. This study is valuable contribution to the Box-Jenkins procedure particularly at the model identification and estimation steps in SARIMA models. Further work involving multiple seasonal ARIMA models, such as short term load data forecasting in certain countries, may provide further insights regarding the subset, multiplicative or additive orders. Keywords: SARIMA; subset; multiplicative; additive; tourist arrivals 2010 Mathematics Subject Classification 62M10; 62P20.