Implementation of Clustering Time Series with DTW to Clustering and Forecasting Rice Prices Each Provinces in Indonesia

Indonesia faces a significant imbalance between domestic supply and demand, leading to escalating rice prices and pronounced regional disparities. To elucidate underlying price patterns and forecast future trends, this study employed Hierarchical Clustering Time-Series with DTW and ARIMA modelling at both individual and cluster levels. Comprehensive analysis, incorporating visualization and threshold comparisons, identified Central Kalimantan as an outlier. Individual ARIMA models demonstrated exceptional performance, with MAPE values below 10%. The clustering time-series correlation using Cophenetic coefficient, reached 0.68 for ward linkages. Two clustering approaches were explored: (1) ignoring the outlier province, (2) excluding Central Kalimantan and incorporating it into a separate cluster. Optimal cluster measurement, the Elbow, Silhouette, Calinski-Harabasz, and Davies-Bouldin, yielded 6-7 clusters for the former approach and 3-5 clusters for the latter. Comparative analysis of individual and cluster forecasts, coupled with paired t-tests, revealed that Ward linkage in the second approach produced the most favorable results, with 27/34 provinces exhibiting cluster MAPE values less than or equal to their individual MAPE. This finding underscores the efficacy of cluster-based modeling in generating accurate and representative estimates for a substantial portion of provinces. A 12-period rice price forecast indicates a prevailing trend of rising prices in most regions of Indonesia.