Forecasting Monthly Rainfall Variability in the Indragiri Region, Indonesia, Using Seasonal ARIMA: Dataset Reconstruction, Model Evaluation, and Out-of-Sample Validation

Cahyo Adi Nugroho

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Keywords:

Abstract

Background: Monthly rainfall forecasting is important for water-resource management, agricultural planning, and hydrometeorological risk assessment. However, reliable forecasting requires a temporally consistent dataset and appropriate representation of seasonal rainfall variability.
Aims: This study aims to reconstruct and audit a monthly rainfall dataset for the Indragiri region, identify its temporal and seasonal characteristics, evaluate alternative Seasonal Autoregressive Integrated Moving Average (SARIMA) models, and assess their forecasting performance and residual adequacy.
Methods: Monthly rainfall data derived from reanalysis were reconstructed for January 2014-June 2025, resulting in 138 monthly records. Temporal auditing identified June 2025 as incomplete, containing only 20 of the expected 60 timestamps; therefore, 137 complete months through May 2025 were used for model development. Autocorrelation and partial autocorrelation analyses were conducted to identify temporal and seasonal structures. Eight SARIMA candidates were compared using AIC, BIC, RMSE, MAE, sMAPE, and Ljung–Box residual diagnostics.
Results: The rainfall series had a mean of 16.15 mm, standard deviation of 13.19 mm, and maximum of 49.59 mm, with strong annual seasonality. SARIMA(0,0,2)(2,1,0)[12] achieved the lowest test RMSE (10.36 mm), MAE (6.98 mm), and sMAPE (48.17%). However, significant residual autocorrelation remained at lags 6, 12, 18, and 24 (p < .001).
Conclusion: The selected SARIMA model provides a useful seasonal forecasting baseline but does not fully capture the dependence structure of monthly rainfall. Forecasts for July 2025–June 2027 indicate persistent seasonal variability, highlighting the need for additional climatic predictors or alternative models to improve forecasting accuracy.
References
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How to Cite

Nugroho, C. A. (2026). Forecasting Monthly Rainfall Variability in the Indragiri Region, Indonesia, Using Seasonal ARIMA: Dataset Reconstruction, Model Evaluation, and Out-of-Sample Validation. Journal of Earth and Planetary System Science, 1(1), 62–74. Retrieved from https://journal.gomit.id/jepss/article/view/181

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[1] Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723. https://doi.org/10.1109/TAC.1974.1100705

[2] Armstrong, J. S. (Ed.). (2001). Principles of forecasting: A handbook for researchers and practitioners. Springer. https://doi.org/10.1007/978-0-306-47630-3

[3] As-syakur, A. R., Adnyana, I. W. S., Mahendra, M. S., Arthana, I. W., Kasa, I. W., Ekayanti, N. W., Nuarsa, I. W., & Sunarta, I. N. (2014). Observation of spatial patterns on the rainfall response to ENSO and IOD over Indonesia using TRMM Multisatellite Precipitation Analysis (TMPA). International Journal of Climatology, 34(15), 3880–3893. https://doi.org/10.1002/joc.3939

[4] Bergmeir, C., Hyndman, R. J., & Koo, B. (2018). A note on the validity of cross-validation for evaluating autoregressive time series prediction. Computational Statistics & Data Analysis, 120, 70–83. https://doi.org/10.1016/j.csda.2017.11.003

[5] Box, G. E. P., & Jenkins, G. M. (1970). Time series analysis: Forecasting and control. Holden-Day.

[6] Box, G. E. P., & Pierce, D. A. (1970). Distribution of residual autocorrelations in autoregressive-integrated moving average time series models. Journal of the American Statistical Association, 65(332), 1509–1526. https://doi.org/10.1080/01621459.1970.10481180

[7] Box, G. E. P., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. (2015). Time series analysis: Forecasting and control (5th ed.). Wiley.

[8] Bridhikitti, A. (2013). Connections of ENSO/IOD and aerosols with Thai rainfall anomalies and associated implications for local rainfall forecasts. International Journal of Climatology, 33(13), 2836–2845. https://doi.org/10.1002/joc.3630

[9] Brockwell, P. J., & Davis, R. A. (2016). Introduction to time series and forecasting (3rd ed.). Springer. https://doi.org/10.1007/978-3-319-29854-2

[10] Chatfield, C. (2000). Time-series forecasting. Chapman & Hall/CRC.

[11] Cleveland, R. B., Cleveland, W. S., McRae, J. E., & Terpenning, I. (1990). STL: A seasonal-trend decomposition procedure based on loess. Journal of Official Statistics, 6(1), 3–73.

[12] Dickey, D. A., & Fuller, W. A. (1979). Distribution of the estimators for autoregressive time series with a unit root. Journal of the American Statistical Association, 74(366a), 427–431. https://doi.org/10.1080/01621459.1979.10482531

[13] Diebold, F. X., & Mariano, R. S. (1995). Comparing predictive accuracy. Journal of Business & Economic Statistics, 13(3), 253–263. https://doi.org/10.1080/07350015.1995.10524599

[14] Gardner, E. S. (1985). Exponential smoothing: The state of the art. Journal of Forecasting, 4(1), 1–28. https://doi.org/10.1002/for.3980040103

[15] Gardner, E. S. (2006). Exponential smoothing: The state of the art—Part II. International Journal of Forecasting, 22(4), 637–666. https://doi.org/10.1016/j.ijforecast.2006.03.003

[16] Gneiting, T., & Katzfuss, M. (2014). Probabilistic forecasting. Annual Review of Statistics and Its Application, 1, 125–151. https://doi.org/10.1146/annurev-statistics-062713-085831

[17] Gneiting, T., & Raftery, A. E. (2007). Strictly proper scoring rules, prediction, and estimation. Journal of the American Statistical Association, 102(477), 359–378. https://doi.org/10.1198/016214506000001437

[18] Gobin, A., Nguyen, H. T., Pham, V. Q., & Pham, H. T. T. (2016). Heavy rainfall patterns in Vietnam and their relation with ENSO cycles. International Journal of Climatology, 36(4), 1686–1699. https://doi.org/10.1002/joc.4451

[19] Hamilton, J. D. (1994). Time series analysis. Princeton University Press.

[20] Harvey, A. C. (1989). Forecasting, structural time series models and the Kalman filter. Cambridge University Press.

[21] Haylock, M. R., Peterson, T. C., Alves, L. M., Ambrizzi, T., Anunciação, Y. M. T., Baez, J., Barros, V. R., Berlato, M. A., Bidegain, M., Coronel, G., Corradi, V., Garcia, V. J., Grimm, A. M., Karoly, D., Marengo, J. A., Marino, M. B., Moncunill, D. F., Nechet, D., Quintana, J., … Vincent, L. A. (2006). Trends in total and extreme South American rainfall in 1960–2000 and links with sea surface temperature. Journal of Climate, 19(8), 1490–1512. https://doi.org/10.1175/JCLI3695.1

[22] Hersbach, H., Bell, B., Berrisford, P., Hirahara, S., Horányi, A., Muñoz-Sabater, J., Nicolas, J., Peubey, C., Radu, R., Schepers, D., Simmons, A., Soci, C., Abdalla, S., Abellan, X., Balsamo, G., Bechtold, P., Biavati, G., Bidlot, J., Bonavita, M., … Thépaut, J.-N. (2020). The ERA5 global reanalysis. Quarterly Journal of the Royal Meteorological Society, 146(730), 1999–2049. https://doi.org/10.1002/qj.3803

[23] Hidayat, R., & Ando, K. (2014). Variabilitas curah hujan Indonesia dan hubungannya dengan ENSO/IOD: Estimasi menggunakan data JRA-25/JCDAS. Agromet, 28(1), 1–8. https://doi.org/10.29244/j.agromet.28.1.1-8

[24] Hurst, H. E. (1951). Long-term storage capacity of reservoirs. Transactions of the American Society of Civil Engineers, 116(1), 770–799. https://doi.org/10.1061/TACEAT.0006518

[25] Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and practice (3rd ed.). OTexts. https://otexts.com/fpp3/

[26] Hyndman, R. J., & Khandakar, Y. (2008). Automatic time series forecasting: The forecast package for R. Journal of Statistical Software, 27(3), 1–22. https://doi.org/10.18637/jss.v027.i03

[27] Hyndman, R. J., & Koehler, A. B. (2006). Another look at measures of forecast accuracy. International Journal of Forecasting, 22(4), 679–688. https://doi.org/10.1016/j.ijforecast.2006.03.001

[28] Hyndman, R. J., Koehler, A. B., Snyder, R. D., & Grose, S. (2002). A state space framework for automatic forecasting using exponential smoothing methods. International Journal of Forecasting, 18(3), 439–454. https://doi.org/10.1016/S0169-2070(01)00110-8

[29] Jolliffe, I. T. (2002). Principal component analysis (2nd ed.). Springer. https://doi.org/10.1007/b98835

[30] Koutsoyiannis, D. (2006). Nonstationarity versus scaling in hydrology. Journal of Hydrology, 324(1–4), 239–254. https://doi.org/10.1016/j.jhydrol.2005.09.022

[31] Kurniadi, A., Weller, E., Min, S.-K., & Seong, M.-G. (2021). Independent ENSO and IOD impacts on rainfall extremes over Indonesia. International Journal of Climatology, 41(6), 3640–3656. https://doi.org/10.1002/joc.7040

[32] Kwiatkowski, D., Phillips, P. C. B., Schmidt, P., & Shin, Y. (1992). Testing the null hypothesis of stationarity against the alternative of a unit root. Journal of Econometrics, 54(1–3), 159–178. https://doi.org/10.1016/0304-4076(92)90104-Y

[33] Leong, M., Juneng, L., Tangang, F., & Salimun, E. (2024). Expansion of winter ENSO-associated rainfall affected area in Southeast Asia under warmer climate. International Journal of Climatology, 44(3), 831–851. https://doi.org/10.1002/joc.8358

[34] Ljung, G. M., & Box, G. E. P. (1978). On a measure of lack of fit in time series models. Biometrika, 65(2), 297–303. https://doi.org/10.1093/biomet/65.2.297

[35] Makridakis, S., & Hibon, M. (2000). The M3-Competition: Results, conclusions and implications. International Journal of Forecasting, 16(4), 451–476. https://doi.org/10.1016/S0169-2070(00)00057-1

[36] Makridakis, S., Spiliotis, E., & Assimakopoulos, V. (2020). The M4 Competition: 100,000 time series and 61 forecasting methods. International Journal of Forecasting, 36(1), 54–74. https://doi.org/10.1016/j.ijforecast.2019.04.014

[37] Mann, H. B. (1945). Nonparametric tests against trend. Econometrica, 13(3), 245–259. https://doi.org/10.2307/1907187

[38] Maraun, D. (2016). Bias correcting climate change simulations—A critical review. Current Climate Change Reports, 2, 211–220. https://doi.org/10.1007/s40641-016-0050-x

[39] McKinney, W. (2010). Data structures for statistical computing in Python. In S. van der Walt & J. Millman (Eds.), Proceedings of the 9th Python in Science Conference (pp. 51–56).

[40] McLeod, A. I., & Li, W. K. (1983). Diagnostic checking ARMA time series models using squared-residual autocorrelations. Journal of Time Series Analysis, 4(4), 269–273. https://doi.org/10.1111/j.1467-9892.1983.tb00373.x

[41] Mori, S., Hamada, J.-I., Tauhid, Y. I., Yamanaka, M. D., Okamoto, N., Murata, F., Sakurai, N., Hashiguchi, H., & Sribimawati, T. (2004). Diurnal land–sea rainfall peak migration over Sumatera Island, Indonesian Maritime Continent, observed by TRMM satellite and intensive rawinsonde soundings. Monthly Weather Review, 132(8), 2021–2039. https://doi.org/10.1175/1520-0493(2004)132<2021:DLRPMO>2.0.CO;2

[42] Nur'utami, M. N., & Hidayat, R. (2016). Influences of IOD and ENSO to Indonesian rainfall variability: Role of atmosphere-ocean interaction in the Indo-Pacific sector. Procedia Environmental Sciences, 33, 196–203. https://doi.org/10.1016/j.proenv.2016.03.070

[43] Partal, T., & Kahya, E. (2006). Trend analysis in Turkish precipitation data. Hydrological Processes, 20(9), 2011–2026. https://doi.org/10.1002/hyp.5993

[44] Petropoulos, F., Apiletti, D., Assimakopoulos, V., Babai, M. Z., Barrow, D. K., Ben Taieb, S., Bergmeir, C., Bessa, R. J., Bijak, J., Boylan, J. E., Browell, J., Carnevale, C., Castle, J. L., Cirillo, P., Clements, M. P., Cordeiro, C., Cyrino Oliveira, F. L., De Baets, S., Dokumentov, A., … Ziel, F. (2022). Forecasting: Theory and practice. International Journal of Forecasting, 38(3), 705–871. https://doi.org/10.1016/j.ijforecast.2021.11.001

[45] Qian, J.-H. (2020). Multi-scale climate processes and rainfall variability in Sumatra and Malay Peninsula associated with ENSO in boreal fall and winter. International Journal of Climatology. https://doi.org/10.1002/joc.6450

[46] Schwarz, G. (1978). Estimating the dimension of a model. The Annals of Statistics, 6(2), 461–464. https://doi.org/10.1214/aos/1176344136

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Research Articles | Vol. 1 Issue 1 (2026) | Published in Sep 16, 2026

Forecasting Monthly Rainfall Variability in the Indragiri Region, Indonesia, Using Seasonal ARIMA: Dataset Reconstruction, Model Evaluation, and Out-of-Sample Validation

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