Robust PCA-Based Multivariate Time Series Clustering for Weekly Indonesian Food Commodity Prices with Missing Data

Abstract

This study proposes an integrated procedure for analyzing multivariate time series (MTS) of strategic food commodity prices across Indonesian regencies/cities, encompassing missing-data imputation, outlier-robust dimensionality reduction, MTS modeling, regional clustering, and cluster-prototype-based forecasting. Weekly price data for eight strategic food commodities across 70 regencies/cities in Indonesia are analyzed through imputation and preprocessing, dimensionality reduction using lag-1 autocovariance-based RPCA (RPCA lag-1), and time series modeling of the lag-1 RPCA principal component scores (RPCA scores) on the first and second principal components (PC1 and PC2) using a first-order vector autoregressive model (VAR(1)) with an intercept term.Regional clustering is performed using non-ensemble methods (K-means Euclidean and PAM Euclidean) to identify the best non-ensemble approach, and Random Forest--General Iterative Clustering (RF-GIC) is also employed as a benchmark. For each clustering result, namely K-means Euclidean as the selected best non-ensemble method and RF-GIC, cluster prototypes are constructed and used for forecasting. The two schemes are compared using a four-fold expanding-window evaluation (root mean square error (RMSE) and mean absolute deviation (MAD)) and a final mean absolute percentage error (MAPE) assessment at 4-step and 26-step horizons, evaluated at both the cluster-prototype and regency/city levels. Based on overall MAPE at the cluster-prototype level, both K-means Euclidean and RF-GIC achieve very accurate performance at the 4-step horizon and accurate performance at the 26-step horizon, with RF-GIC yielding lower overall MAPE than K-means Euclidean at both horizons. At the regency/city level, both methods fall into the accurate category at the 4-step horizon and the moderately accurate category at the 26-step horizon, with only a small difference in overall MAPE (slightly lower for K-means Euclidean). The decrease in accuracy is primarily driven by longer forecasting horizons and commodity-specific volatility, particularly for bird’s-eye chili and red chili.