Multivariate Time Series Forecasting of KP-RI Financial Performance Using VARIMA and VARIMAX with a Dummy Variable - Tri Candra Nur Muhaimin; Nurjannah Nurjannah; Rahma Fitriani (CAUCHY: Jurnal Matematika Murni dan Aplikasi, 2026)
Cooperative financial performance is influenced by both internal financial dynamics and external policy interventions. However, the contribution of policy-intervention information to multivariate forecasting models in cooperative finance remains insufficiently explored. This study compares Vector Autoregressive Integrated Moving Average (VARIMA) and Vector Autoregressive Integrated Moving Average with Exogenous Variables (VARIMAX-Dummy) models for analyzing and forecasting monthly Interest Income (PHB) and Net Surplus (SHU) in a savings and loan cooperative during 2015–2024. The analysis employed stationarity testing, cointegration testing, model identification, Granger causality analysis, Impulse Response Function, Forecast Error Variance Decomposition, and out-of-sample forecasting evaluation. A pulse dummy variable representing mandatory savings policy adjustments was incorporated into the VARIMAX model. The results indicate bidirectional predictive relationships and stable dynamic responses in both models. Model identification indicated that VARIMA(1,1,0) provided the optimal endogenous dynamic structure, which was subsequently retained in the VARIMAX-Dummy resulting VARIMAX (1,1,0)-Dummy specification. Forecasting evaluation showed that the VARIMAX-Dummy model achieved lower RMSE values for SHU (0.2129) and PHB (0.2088) than the corresponding VARIMA model (0.7434 and 0.6060). These findings demonstrate that incorporating policy-intervention information improves forecasting accuracy and enhances the representation of cooperative financial dynamics. The study highlights the value of exogenous policy variables in multivariate forecasting models for cooperative financial management.