Forecasting indonesia's non-oil and gas exports and imports using the vector autoregressive integrated moving average (VARIMA) model - Sifha Desti Wulandari; Madona Yunita Wijaya; Irma Fauziah (Jurnal Absis: Jurnal Pendidikan Matematika dan Matematika, 2026)
Indonesia’s international trade, particularly in the non-oil and gas sector, plays a significant role in the national economy. This study aims to model and forecast Indonesia’s non-oil and gas exports and imports using the Vector Autoregressive Integrated Moving Average (VARIMA) model, a multivariate time series method that considers dynamic interdependence between variables. The data used in this study were monthly data from January 2018 to December 2024, consisting of 84 observations divided into 58 training data and 26 testing data. Model order identification was carried out using the Matrix Autocorrelation Function (MACF) for the MA component and the Matrix Partial Autocorrelation Function (MPACF) for the AR component. Parameter estimation was conducted using Maximum Likelihood Estimation (MLE) and refined through a restriction process to retain only statistically significant parameters. Diagnostic tests showed that the residuals met the assumptions of white noise and multivariate normality. Among several candidate models, VARIMA(2,1,2) was selected as the optimal model based on the balance between information criteria, model complexity, parameter stability, and forecasting reliability. The model produced MAPE values of 11.10% for imports, categorized as good, and 8.81% for exports, categorized as very good. The forecast results showed relatively stable fluctuations, with imports projected to range from US$14.32 million to US$18.48 million and exports from US$18.38 million to US$26.41 million. These findings indicate that the VARIMA(2,1,2) model provides adequate forecasting performance and can serve as a quantitative basis for supporting foreign trade policy planning, particularly in anticipating the dynamics of Indonesia’s non-oil and gas exports and imports.