Comparative Analysis of ARIMA and Fourier Series Methods for Air Temperature Forecasting in Surabaya

Annas Thasya Haafizhah  Salsabiila; Regita Putri Permata; Sri Hidayati

doi:10.59395/ijadis.v6i3.1415

Authors

Annas Thasya Haafizhah Salsabiila Telkom University Surabaya
Regita Putri Permata Telkom University Surabaya
Sri Hidayati Telkom University Surabaya

DOI:

https://doi.org/10.59395/ijadis.v6i3.1415

Keywords:

Air Temperature, ARIMA, Fourier Series, ARIMA Fourier, Time Series

Abstract

Urban climate change, particularly rising temperatures and the Urban Heat Island (UHI) phenomenon, poses challenges for cities like Surabaya, Indonesia. This study compares the forecasting performance of ARIMA and ARIMA-Fourier models using daily air temperature data from 2020 to 2024. The analysis involved stationarity testing, model estimation, and evaluation across four forecasting horizons. ARIMA models (especially ARIMA(0,1,1) and ARIMA(1,1,0)) showed reliable short-term forecasts, but were less effective in capturing seasonal patterns. To address this, Fourier terms were integrated into the ARIMA framework. The ARIMA-Fourier model achieved better accuracy and higher R² values in short- and medium-term forecasts, particularly with an oscillation parameter of k = 150. However, its performance declined in long-term predictions due to overfitting risks. Overall, the ARIMA-Fourier model is more adaptive for capturing complex temperature seasonality and can support more accurate urban climate forecasting in Surabaya.

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References

[1] G. K. Hamdani, V. D. Rikumahu, F. E. Putra, and C. Uny, “Fenomena Urban Heat Island di Kota Bandung,” Edusaintek: Jurnal Pendidikan, Sains dan Teknologi, vol. 12, no. 2, pp. 629–644, Feb. 2025.

[2] I. Putri et al., “Peramalan Rata-Rata Temperatur Udara Tahunan di Indonesia Periode 2022-2031.” [Online]. Available: http://envirotek.upnjatim.ac.id/

[3] R. Gita Alfitri, “Peramalan Temperatur Rata-rata dan Kelembaban Rata-rata Harian Kabupaten Seram Bagian Timur Menggunakan ARIMA Box-Jenkins”, doi: 10.12962/j27213862.vxix.xxxx.

[4] B. E. Bhaskara and R. A. Pratomo, “Perkembangan Fenomena Urban Heat Island di Kota Samarinda,” Jurnal Wilayah dan Lingkungan, vol. 11, no. 1, pp. 22–35, Apr. 2023, doi: 10.14710/jwl.11.1.22-35. DOI: https://doi.org/10.14710/jwl.11.1.22-35

[5] A. Alauddin and T. Mustamin, “Karakteristik Temperatur Udara Terhadap Kenyamanan Termal Di Masjid Agung Luwuk Banggai,” Jurnal Linears, vol. 2, no. 2, pp. 49–54, Feb. 2020, doi: 10.26618/j-linears.v2i2.3121. DOI: https://doi.org/10.26618/j-linears.v2i2.3121

[6] Susilawati, “DAMPAK PERUBAHAN IKLIM TERHADAP KESEHATAN.”

[7] D. O. A. Putri, M. Ermawati, and N. P. Yanto, “ANALISIS DAMPAK PERUBAHAN PENGGUNAN LAHAN PERKOTAAN TERHADAP URBAN HEAT ISLAND DI KECAMATAN KEDATON,” Jurnal Perencanaan dan Pengembangan Kebijakan, vol. 4, no. 1, p. 27, Apr. 2024, doi: 10.35472/jppk.v4i1.1464. DOI: https://doi.org/10.35472/jppk.v4i1.1464

[8] Muliadi, I. Nugraha, and F. Dalila, “ANALISIS URBAN HEAT ISLAND MENGGUNAKAN CITRA LANDSAT DI KOTA PEKANBARU,” Journal of Urban and Regional Planning for Sustainable Environment (JURPS), vol. 3, no. 1, p. 28284, Feb. 2024. DOI: https://doi.org/10.25299/jurps.2024.17874

[9] A. Y. Pratiwi and L. M. Jaelani, “Analisis Perubahan Distribusi Urban Heat Island (UHI) di Kota Surabaya Menggunakan Citra Satelit Landsat Multitemporal,” JURNAL TEKNIK ITS, vol. 9, no. 2, pp. C48–C54, 2020, Accessed: Jun. 28, 2025. [Online]. Available: 10.12962/j23373539.v9i2.53982 DOI: https://doi.org/10.12962/j23373539.v9i2.53982

[10] T. Purwa and B. Ngwarati, “Assessing Forecasting Performance of Daily Mean Temperature at 1st and 2nd Perak Station, Surabaya Using ARIMA and VARIMA Model with Outlier Detection,” Jambura Journal of Mathematics, vol. 4, no. 1, Jan. 2022, doi: 10.34312/jjom.v4i1.11975. DOI: https://doi.org/10.34312/jjom.v4i1.11975

[11] M. F. Zulfikar, R. H. Virgianto, and Q. A. Kartika, “Pengaruh Urban Heat Island terhadap Kenyamanan di Jakarta,” The Climate of Tropical Indonesia Maritime Continent Journal, vol. 1, no. 1, pp. 34–57, Apr. 2022.

[12] R. P. Permata, A. Muhaimin, and S. Hidayati, “RAINFALL FORECASTING WITH AN INTERMITTENT APPROACH USING HYBRID EXPONENTIAL SMOOTHING NEURAL NETWORK,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 18, no. 1, pp. 0457–0466, Mar. 2024, doi: 10.30598/barekengvol18iss1pp0457-0466. DOI: https://doi.org/10.30598/barekengvol18iss1pp0457-0466

[13] C. Fan, “Global Temperature Anomaly Forecast: A Comparative Analysis of ARIMA and ETS Models,” in Advances in Economics, Management and Political Sciences, 2024, pp. 70–76. doi: 10.54254/2754-1169/144/2024.GA19089. DOI: https://doi.org/10.54254/2754-1169/2024.GA19089

[14] K. Li, “Prediction of atmospheric temperature in Sacramento area based on ARIMA and ETS models,” Theoretical and Natural Science, vol. 51, no. 1, pp. 165–171, Nov. 2024, doi: 10.54254/2753-8818/51/2024ch0197. DOI: https://doi.org/10.54254/2753-8818/51/2024CH0197

[15] D. Liu et al., “Slope Micrometeorological Analysis and Prediction Based on an ARIMA Model and Data-Fitting System,” Sensors, vol. 22, no. 3, Feb. 2022, doi: 10.3390/s22031214. DOI: https://doi.org/10.3390/s22031214

[16] H. KOÇAK, “Time Series Prediction of Temperature Using Seasonal ARIMA and LSTM Models,” Gazi Journal of Engineering Sciences, vol. 9, no. 3, pp. 574–584, Jan. 2024, doi: 10.30855/gmbd.0705088. DOI: https://doi.org/10.30855/gmbd.0705088

[17] Yusrini, D. Firmayasari, Hukmah, and Suriani, “Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika,” Proximal: Jurnal Penelitian Matematika dan Pendidikan Matematika, vol. 7, pp. 961–974, Aug. 2024, doi: 10.30605/proximal.v5i2.4518. DOI: https://doi.org/10.30605/proximal.v7i2.4518

[18] W. Palma, TIME SERIES ANALYSIS, 1st ed. John Wiley & Sons, 2016.

[19] G. Kermarrec, F. Maddanu, A. Klos, T. Proietti, and J. Bogusz, “Modeling trends and periodic components in geodetic time series: a unified approach,” J Geod, vol. 98, no. 3, Mar. 2024, doi: 10.1007/s00190-024-01826-5. DOI: https://doi.org/10.1007/s00190-024-01826-5

[20] A. K. Rahma, Q. Z. Abidin, J. K. Prasetyo, B. Larasati, D. Amelia, and N. Chamidah, “PREDICTION OF CRUDE OIL PRICES IN INDONESIA USING FOURIER SERIES ESTIMATOR AND ARIMA METHOD,” BAREKENG: Jurnal Ilmu Matematika dan Terapan, vol. 18, no. 3, pp. 1673–1682, Jul. 2024, doi: 10.30598/barekengvol18iss3pp1673-1682. DOI: https://doi.org/10.30598/barekengvol18iss3pp1673-1682

[21] S. Karamolegkos and D. E. Koulouriotis, “Advancing short-term load forecasting with decomposed Fourier ARIMA: A case study on the Greek energy market,” Energy, vol. 325, Jun. 2025, doi: 10.1016/j.energy.2025.135854. DOI: https://doi.org/10.1016/j.energy.2025.135854

[22] G. Perone, “Comparison of ARIMA, ETS, NNAR, TBATS and hybrid models to forecast the second wave of COVID-19 hospitalizations in Italy,” European Journal of Health Economics, vol. 23, no. 6, pp. 917–940, Aug. 2022, doi: 10.1007/s10198-021-01347-4. DOI: https://doi.org/10.1007/s10198-021-01347-4

[23] O. Yakubu and C. Narendra Babu, “Electricity consumption forecasting using DFT decomposition based hybrid ARIMA-DLSTM model,” Indonesian Journal of Electrical Engineering and Computer Science, vol. 24, no. 2, pp. 1107–1120, Nov. 2021, doi: 10.11591/ijeecs.v24.i2.pp1107-1120. DOI: https://doi.org/10.11591/ijeecs.v24.i2.pp1107-1120

[24] L. R. Olsen, S. H. Sørbye, and F. Godtliebsen, “A scale-space approach for detecting non-stationarities in time series,” Scandinavian Journal of Statistics, vol. 35, no. 1, pp. 119–138, Mar. 2008, doi: 10.1111/j.1467-9469.2006.00556.x. DOI: https://doi.org/10.1111/j.1467-9469.2006.00556.x

[25] J. Zhang, Y. Yang, and J. Ding, “Information criteria for model selection,” Sep. 01, 2023, John Wiley and Sons Inc. doi: 10.1002/wics.1607. DOI: https://doi.org/10.1002/wics.1607