Seasonal time series forecasting of Indonesian railway passengers: A comparison of Holt–Winters and SARIMA

Gita Indah Cahyani; Besse Arnawisuda Ningsi; Irvana Arofah

doi:10.30821/axiom.v15i1.25570

Seasonal time series forecasting of Indonesian railway passengers: A comparison of Holt–Winters and SARIMA

Gita Indah Cahyani, Besse Arnawisuda Ningsi, Irvana Arofah

Abstract

Managing the number of railway passengers in Indonesia presents a significant challenge for PT Kereta Api Indonesia, particularly in relation to transport capacity planning, scheduling, and resource optimization. Forecasting therefore plays a crucial role in supporting effective decision-making. This study aimed to forecast railway passenger volumes using the Holt–Winters Triple Exponential Smoothing method and the Seasonal Autoregressive Integrated Moving Average (SARIMA) model, and to compare their forecasting performance. This applied research utilized secondary monthly data published by Statistics Indonesia (BPS), covering the period from January 2022 to December 2024, with forecasts generated for January to June 2025. Model performance was evaluated using the Mean Absolute Percentage Error (MAPE) criterion. The results indicated that the SARIMA model outperformed the Holt–Winters variants and other SARIMA specifications, achieving the lowest MAPE value of approximately 3%. Based on this evaluation, the SARIMA model was identified as the most accurate model for forecasting Indonesian railway passenger volumes. The findings suggest that SARIMA-based models provide a reliable approach for supporting railway passenger demand forecasting in Indonesia.

Keywords

Forecasting, Holt–Winters; Indonesian railway; SARIMA; Time Series

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References

Aslam, A.P. (2023). Buku ajar metodologi penelitian. Sukoharjo: Tahta Media Group.

Aswi, & Sukarna. (2006). Analisis deret waktu analisis deret waktu: teori dan aplikasi. Makasar: Andira.

Chuwang, D.D., & Chen, W. (2022). Forecasting daily and weekly passenger demand for urban rail transit stations based on a time series model approach. Forecasting, 4(4), 904–924. https://doi.org/10.3390/forecast4040049

Devianto, D., Permana, D., Arif, E., Afrimayani, A., Yanuar, F., Maiyastri, M., & Yollanda, M. (2024). An innovative model for capturing seasonal patterns of train passenger movement using exogenous variables and fuzzy time series hybridization. Journal of Open Innovation: Technology, Market, and Complexity, 10(1), 1–14. https://doi.org/10.1016/j.joitmc.2024.100232

Dewi, N.P., & Listiowarni, I. (2020). Implementasi holt-winters exponential smoothing untuk peramalan harga bahan pangan di kabupaten pamekasan. Digital Zone: Jurnal Teknologi Informasi & Komunikasi, 11(2), 219–231. https://doi.org/10.31849/digitalzone.v11i2.4797

Enders, W. (2014). Applied econometric time series. Hokoben: Wiley.

Fahik, D.S., & Jatipaningrum, M.T. (2021). Peramalan jumlah penumpang penerbangan internasional di bandar udara internasional soekarno hatta dengan metode holt-winters exponential smoothing dan seasonal arima. Jurnal Statistika Industri Dan Komputasi, 6(1), 77–87. https://garuda.kemdiktisaintek.go.id/documents/detail/4122906

Gunawan, J.R., & Cahyono, M.S.D. (2023). Analisis jumlah pengguna kereta api komuter sidoarjo-indro. Jurnal Anggapa, 2(1), 41–45. https://doi.org/10.61293/anggapa.v2i2.622

Harahap, F.R., & Darnius, O. (2022). Optimization of holt-winters exponential smoothing parametes using the golden section and dichotomous search method. FARABI: Jurnla Matematika Dan Pendidikan Matematika, 5(2), 104–115. https://doi.org/10.47662/farabi.v5i2.385

Hartono, B., Khakim, M.A., & Rakhmawati, N.A. (2020). Analisis data kereta api dan stasiun pada daerah operasi viii surabaya menggunakan sparql dengan algoritma betweenness centrality. Cogito Smart Journal, 6(2), 128–140. https://doi.org/10.31154/cogito.v6i2.232.128-140

Khoiri, H.A. (2023). Analisis deret waktu univariat: Teori dan Pengolahan Data Senin. Surabaya: UNIPMA Press.

Li, W., Sui, L., Zhou, M., & Dong, H. (2021). Short-term passenger flow forecast for urban rail transit based on multi-source data. Eurasip Journal on Wireless Communications and Networking, 2021(1), 1–13. https://doi.org/10.1186/s13638-020-01881-4

Makridakis, S.G., Wheelwright, S.C., Wheelwright, Steven C., A., & McGee, V.E. (1991). Metode dan aplikasi peramalan. Erlangga.

Malki, A., Atlam, E., Ella, A., Ewis, A., Dagnew, G., & Gad, I. (2022). Sarima model-based forecasting required number of covid-19 vaccines globally and empirical analysis of peoples ’ view towards the vaccines. Alexandria Engineering Journal, 61(12), 12091–12110. https://doi.org/10.1016/j.aej.2022.05.051

Midiyanti, R., & Ramlan, J.S. (2020). Penerapan manajemen fasilitas dan smart mobility di pt. kereta api inodonesia (persero). Jurnal Manajemen Aset Infrastruktur & Fasilitas, 4(1), 67–76. https://doi.org/10.12962/j26151847.v4i1.6834

Milenkovic, M., Svadlenka, L., Melichar, V., Bojovic, N., & Avramovic, Z. (2016). Sarima modelling approach for railway passenger flow forecasting. Transport, 1(1), 1–8. https://doi.org/10.3846/16484142.2016.1139623

Negara, R.I.P. (2021). Peramalan jumlah penumpang kapal di pelabuhan pantai baru dengan metode sarima dan winter’s exponential smoothing. BPS Provinsi NTT: Jurnal Statistika Terapan, 1(1), 63–78. https://jstar.id/ojs/indeks.php/JSTAR/article/view/5

Prianda, B.G., & Widodo, E. (2021). Perbandingan metode seasonal arima dan extreme learning machine pada peramalan jumlah wisatawan mancanegara ke bali. BAREKENG: Jurnal Ilmu Matematika Dan Terapan, 15(4), 639–650. https://doi.org/10.30598/barekengvol15iss4pp639-650

Romaita, D., Bachtiar, F.A., & Furqon, M.T. (2019). Perbandingan metode exponential smoothing untuk peramalan penjualan produk olahan daging ayam kampung (studi kasus: ayam goreng mama arka). Jurnal Pengembangan Teknologi Informasi Dan Ilmu Komputer, 3(11), 10384–10392. http://j-ptiik.ub.ac.id

Saputro, D.W., Agustuana, D. S., Sabina, F.D., Nuarni, L., P.Manullang, R., Shavira, T., Alvionita, M., & Muthoharoh, L. (2023). Predicting the number of train passengers in java island using sarima model. EKSAKTA: Journal of Sciences and Data Analysis, 4(2), 40–48. https://doi.org/10.20885/eksakta.vol4.iss2.art5

Suhartono. (2008). Analisis data statistik dengan r. Surabaya: Lab. Statistik Komputasi.

Susanti, N.E., Saputra, R., & Situmorang, I.A. (2024). Perbandingan metode sarima, double exponential smoothing dan holt-winter additive dalam peramalan retail sales mobil honda. JSMS: Jurnal Sains Matematika Dan Statistika, 10(1), 58–70. https://doi.org/10.24014/jsms.v10i1.26375

Tambuwun, P.F.A., Nainggolan, N., & Langi, Y.A.R. (2023). Peramalan banyaknya penumpang bandar udara internasional sam ratulangi manado dengan metode winter’s exponential smoothing dan seasonal arima. D’Cartesian: Jurnal Matematika Dan Aplikasi, 12(1), 14–20. https://doi.org/10.35799/dc.12.1.2023.48066

Tripena, A., & Amru, D. (2024). Analisis perbedaan jumlah penumpang kereta api pada bulan yang memiliki hari libur terbanyak dan paling sedikit di stasiun purwokerto 2023. Ulil Albab : Jurnal Ilmiah Multidisiplin, 3(8), 803–816. https://doi.org/10.56799/jim.v3i8.5027

Triwijaya, S., E.W, A.P., & D.P, A.F. (2018). Multistage desain instalasi equipment room stasiun mandalle berdasarkan karakteristik beban. Jurnal Geuthee: Penelitian Multidisiplin, 5(2), 235–245. https://doi.org/10.52626/jg.v5i2.171

Wei, W.W.S. (2006). Time series analysis: univariate and multivariate methods. California: Pearson Addison Wesley.

Yuliana, Tasari, Setiyaningsih, A., Munif, F.A., & Putri, M.F. (2022). Optimalisasi biaya transportasi produk umkm naturies indonesia dengan metode northwest corner dan vogel’s approximation. Jurnal Derivat: Jurnal Matematika Dan Pendidikan Matematika, 9(2), 246–257. https://doi.org/10.31316/jderivat.v9i2.3138

Zuo, T., Tang, S., Zhang, L., Kang, H., Song, H., & Li, P. (2025). An enhanced timesnet-sarima model for predicting outbound subway passenger flow with decomposition techniques. Applied Sciences (Switzerland), 15(6), 1–25. https://doi.org/10.3390/app15062874

DOI: http://dx.doi.org/10.30821/axiom.v15i1.25570