Subset Sarima Modelling: An Alternative Definition and a Case Study
Ette Harrison Etuk *
Department of Mathematics and Computer Science, Rivers State University of Science and Technology, Port Harcourt, Nigeria.
Nathaniel Ojekudo
Department of Computer Science, Ignatius Ajuru University of Education, Port Harcourt, Nigeria.
*Author to whom correspondence should be addressed.
Abstract
Aims: To provide an alternative definition for subset Sarima modeling and demonstrate it by application to monthly internally generated revenue of Ikot Ekpene Local Government Area of Akwa Ibom State of Nigeria.
Study Design: The study design is theoretical as well as empirical.
Place and Duration of Study: Department of Mathematics and Computer Science, Rivers State University of Science and Technology, Port Harcourt, Nigeria.
Methodology: Based on the duality relationship between autoregressive (AR) and moving average (MA) models an alternative definition to subset sarima models is proposed. The seasonality of the above-mentioned time series is established. A non-seasonal differencing of the seasonal difference of the series yields a stationary series which is analysed by Sarima methods.
Results: Applying the duality relationship between AR and MA models, subset Sarima models may be defined in AR terms rather than exclusively in MA terms as earlier done. An analysis of a 120-point internally generated revenue series from 1998 to 2007 yields the additive model from the original SARIMA (1, 1, 0)x(1, 1, 0)12 model. The additive model is found to be adequate.
Conclusion: Based on the new and equivalent definition the monthly internally generated revenue of Ikot Ekpene Local Government Area of Nigeria follows an additive Sarima Model.
Keywords: Sarima model, subset sarima model, additive sarima model,, multiplicative sarima model, internally generated revenue, Ikot Ekpene LGA, Nigeria.