Generalized Space-Time Autoregressive Moving Average Model with Rainfall as Exogenous Variable for Inflation Data in Sulawesi Island - Rahman, Muhammad Fatur; Ihsan, Hisyam; Sanusi, Wahidah (Jurusan Matematika FMIPA UNM, 2025)
The Generalized Space-Time Autoregressive Moving Average with Exogenous Variables (GSTARMAX) model is an extension of the Generalized Space-Time Autoregressive Moving Average (GSTARMA) model, incorporating an exogenous variable (X) to enhance model accuracy while accounting for external factors. The advantage of the GSTARMAX model is its ability to accommodate location heterogeneity and generate a picture of an event for several future periods while considering other factors outside the scope of observation. This study applies the GSTARMAX model approach to analyze inflation data in Sulawesi Island, considering rainfall as an exogenous variable. Given the extreme and unpredictable climate changes, particularly rainfall in the Sulawesi region, which have become an annual phenomenon in recent years. This not only impacts community activities but also triggers uncertainty in future inflation. Uncontrolled inflation affects the decline in purchasing power, increases production costs, and disrupts goods distribution. Therefore, the objective of this study is to develop a model that can describe inflation in Sulawesi Island based on historical inflation and rainfall data. This study discusses the application of the Generalized Space-Time Autoregressive Moving Average with Exogenous Variables (GSTARMAX) model to analyze inflation in Sulawesi Island during the period 2020-2024. The data collected are from six provinces in Sulawesi Island: South Sulawesi, Southeast Sulawesi, West Sulawesi, Central Sulawesi, North Sulawesi, and Gorontalo. This study uses inverse distance weighting and cross-correlation normalization to build the model. The results indicate that the GSTARMAX (11;0;0) (1;2;0) or GSTARX (11) (1;2;0) model using cross-correlation normalization weights is the best model for inflation data in Sulawesi Island, with residuals that meet the white noise assumption. This means the model can be used to forecast future inflation.