Calendar variation model based on ARIMAX for forecasting sales data with Ramadhan effect

Abstract

Many economics and business data are compiled each month and are available as monthly time series. Such time series may be subjected to two kinds of calendar effects, namely trading day and holiday effects. The objective of this research is to develop a calendar variation model based on ARIMAX method for forecasting sales data with Ramadhan effect. In most Islamic countries, the trade activities frequently contain calendar variation pattern due to the consumption to certain products usually follows lunar calendar, instead of following common solar calendar. Firstly, this research focuses on the development of model building procedure to find the best calendar variation model. In this ARIMAX method, the deterministic and stochastic trends are examined. The procedure for fitting the ARIMAX model consists of only modeling calendar variation effect, its error, and adaptively combining the calendar variation effect and ARIMA model. This procedure is applied in modeling and forecasting of sales data, i.e. the monthly sales of Moslem boys’ clothes in Indonesia. The results show that the proposed model yields better forecast at out-sample data compared to the Decomposition method and Seasonal ARIMA, and Neural Networks.