Peramalan Harga Batubara Acuan dengan Fuzzy Time Series Lee dan Evaluasi Out-of-Sample

Abstract

The Reference Coal Price (Harga Batubara Acuan, HBA) exhibits substantial fluctuations, making reliable forecasting important for planning and decision-making in the coal industry. This study applies the Lee Fuzzy Time Series (FTS Lee) method to forecast HBA and evaluates its in-sample and out-of-sample accuracy. Monthly HBA data from January 2020 to December 2024 were used for model development, with linear interpolation applied to construct additional historical observations. The forecasting procedure involved determining the universe of discourse, establishing fuzzy intervals, fuzzification, forming Fuzzy Logical Relationships and Fuzzy Logical Relationship Groups, and defuzzification. A sensitivity analysis compared models developed from 60 original observations and 119 observations including interpolated values. The reported in-sample evaluation yielded an MSE of 81.94, an MAD of 6.48, and a MAPE of 4.80%. The interpolated-data model produced a fixed projection of USD 125/ton for the 2025 evaluation period, with an out-of-sample MSE of 338.65, an MAD of 15.88, and a MAPE of 15.35%. In comparison, the model based on original observations achieved a MAPE of 12.05%, while a fixed-value naive benchmark achieved a MAPE of 13.53%. These findings indicate that linear interpolation did not improve out-of-sample accuracy under the evaluated configuration and that FTS Lee did not outperform the naive benchmark. The results highlight the importance of independent out-of-sample evaluation and the limitations of fixed-value forecasting under changing market conditions.