Application of the Box-Jenkins Methodology in Forecasting Monthly Electrical Energy Consumption in the Province of Nueva Vizcaya, Philippines: A Comparative Evaluation of Arima and Sarima Models

Alberto M. Camangian^1,

¹Saint Mary’s University, School of Graduate Studies, Nueva Vizcaya, Philippines

Cite this paper:
Alberto M. Camangian. Application of the Box-Jenkins Methodology in Forecasting Monthly Electrical Energy Consumption in the Province of Nueva Vizcaya, Philippines: A Comparative Evaluation of Arima and Sarima Models. International Journal of Econometrics and Financial Management. 2026; 13(1):9-19. doi: 10.12691/ijefm-13-1-2

Abstract

As electricity demand continues to grow, accurate consumption forecasting has become an increasingly important foundation for efficient energy planning, especially at the provincial level where local demand drivers differ significantly from national trends. This study forecasted the monthly electrical energy consumption of the Province of Nueva Vizcaya, Philippines, from January 2016 to December 2025 using Autoregressive Integrated Moving Average (ARIMA) and Seasonal Autoregressive Integrated Moving Average (SARIMA) models developed through the Box–Jenkins methodology. Unlike previous studies that relied on partial datasets, this study used the complete sectoral dataset covering all eight consumer categories, Commercial, Special Purpose Lighting, Public Building, Residential, Non-Lighting, Street Lights, Industrial, and High Voltage, with an average monthly consumption of 113,802 kWh. The analysis revealed a clear upward trend of approximately 11.1% over ten years alongside a stable and recurring seasonal pattern, with consumption consistently peaking between May and September during the dry season. Stationarity was achieved through log transformation, one regular difference (d=1), and one seasonal difference (d=1). Among all candidate models evaluated, ARIMA(3,1,2) recorded the lowest AIC (−701.44) and BIC (−684.76) but failed the residual diagnostic check due to significant autocorrelation in its residuals. SARIMA(0,1,1)(0,1,2)₁₂ passed all diagnostic checks with a Ljung–Box p-value of 0.5367 and achieved superior out-of-sample accuracy with RMSE of 0.01014 and MAPE of 0.0555 and was therefore selected as the best-fitting model. The 12-month forecasts for 2026 project monthly electrical energy consumption between 121,527.40 kWh and 126,178.50 kWh, providing reliable demand projections to support energy supply planning, budget management, and the province's ongoing transition toward renewable energy sources in alignment with SDG 7 and SDG 13.

Keywords:
ARIMA SARIMA Box-Jenkins Methodology Electrical Energy Consumption Non-Stationary Time Series Forecasting Nueva Vizcaya Philippines

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References:

[1]	Samuel, J. (2022). Forecasting electricity consumption in the Philippines using ARIMA models. International Journal of Machine Learning and Computing, 12(6).
[2]	Urrutia, J. D., Resurreccion, N. C., Visco, L. M. C., Bautista, L. A., Malvar, R. J., Oliquino, A. B., & Gano, L. A. (2018). Daily prediction of electricity rates of distribution utilities in Luzon. Indian Journal of Science and Technology, 11(20), 1–8.
[3]	International Energy Agency. (2023). World energy outlook 2023. IEA. https://www.iea.org/reports/world-energy-outlook-2023.
[4]	International Energy Agency. (2020). Global energy review 2020: The impacts of the Covid-19 crisis on global energy demand and CO₂ emissions. IEA. https://www.iea.org/reports/global-energy-review-2020.
[5]	Department of Energy. (2020). Philippine energy situation: 2020 annual report. DOE. https://www.doe.gov.ph.
[6]	United Nations. (2015). Transforming our world: The 2030 agenda for sustainable development. United Nations. https://sdgs.un.org/2030agenda.
[7]	Torculas, E., Rentillo, E. J., & Ambita, A. A. (2023). Forecasting of energy consumption in the Philippines using machine learning algorithms. In Communications in computer and information science (pp. 424–435).
[8]	Ortigoza-Larroza, C., Rivas-Martínez, G. I., Grillo, S., & Benítez, E. (2025). Residential Electricity Consumption Forecasting using Machine Learning and SARIMA Approaches: A Case Study of Paraguay. International Journal of Energy and Water Resources, 10(1).
[9]	Ramos, P. V. B., Villela, S. M., Silva, W. N., & Dias, B. H. (2023). Residential energy consumption forecasting using deep learning models. Applied Energy, 350, 121705.
[10]	Nazir, A., Shaikh, A. K., Shah, A. S., & Khalil, A. (2023). Forecasting energy consumption demand of customers in smart grid using Temporal Fusion Transformer (TFT). Results in Engineering, 17, 100888.
[11]	Amalou, I., Mouhni, N., & Abdali, A. (2022). Multivariate time series prediction by RNN architectures for energy consumption forecasting. Energy Reports, 8, 1084–1091.
[12]	Pierre, A. A., Akim, S. A., Semenyo, A. K., & Babiga, B. (2023). Peak Electrical Energy Consumption Prediction by ARIMA, LSTM, GRU, ARIMA-LSTM and ARIMA-GRU approaches. Energies, 16(12), 4739.
[13]	Klyuev, R. V., Morgoev, I. D., Morgoeva, A. D., Gavrina, O. A., Martyushev, N. V., Efremenkov, E. A., & Mengxu, Q. (2022). Methods of Forecasting Electric Energy Consumption: A Literature review. Energies, 15(23), 8919.
[14]	Jalambo, M., Saquin, P. L., Dalis, I., Saumat, M., Rupinta, M., & Demecillo, G. (2025). Analysis and forecasting of electricity demand in MOELCI-II using ARIMA Model. International Journal for Multidisciplinary Research, 7(4).
[15]	Arumugam, V., & Natarajan, V. (2023). Time series modeling and forecasting using autoregressive integrated moving average and seasonal autoregressive integrated moving average models. Instrumentation Mesure Métrologie, 22(4), 161–168.
[16]	Hossain, M. L., Shams, S. M. N., & Ullah, S. M. (2025). Time-series and deep learning approaches for renewable energy forecasting in Dhaka: a comparative study of ARIMA, SARIMA, and LSTM models. Discover Sustainability, 6(1).
[17]	Box, G.E., Jenkins, G.M., Reinsel, G.C. and Ljung, G.M. (2015) Time Series Analysis: Forecasting and Control. John Wiley & Sons, Hoboken.
[18]	Delima, A. J. P. (2019). Application of time series analysis in projecting Philippines’ electric consumption. International Journal of Machine Learning and Computing, 9(5), 694–699.
[19]	Parreno, S. J. (2023). Forecasting the total non-coincidental monthly system peak demand in the Philippines: a comparison of seasonal autoregressive integrated moving average models and artificial neural networks. International Journal of Energy Economics and Policy, 13(5), 544–552.
[20]	Domingo, C. J. (2024). Electrical energy consumption models in the province of Nueva Vizcaya (Unpublished thesis).
[21]	Tolentino, J. A. (2025). Forecasting electricity consumption using ARIMA model. In Lecture notes in networks and systems (pp. 41–51).
[22]	Mahusay, A. T., & Fenomeno, S. D. (2022). Electricity Consumption Prediction Model for Southern Luzon State University-Main Campus using Artificial Neural Network. 2022 IEEE 12th Annual Computing and Communication Workshop and Conference (CCWC), 3, 0038–0044.
[23]	Nueva Vizcaya, Philippines. (2025). Physiological features and natural Resources - Nueva Vizcaya, Philippines. Nueva Vizcaya, Philippines - Naturally Vibrant and Watershed Haven of the Cagayan Valley. https://nuevavizcaya.gov.ph/physiological-features-and-natural-resources/.
[24]	Philippine Statistics Authority. (2020). 2020 census of population and housing: Nueva Vizcaya provincial profile. PSA. https://www.psa.gov.ph.
[25]	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.
[26]	Kwiatkowski, D., Phillips, P.C.B., Schmidt, P. and Shin, Y. (1992) Testing the Null Hypothesis of Stationarity against the Alternative of a Unit Root. Journal of Econometrics, 54, 159-178.
[27]	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.
[28]	Box, G. E. P., & Cox, D. R. (1964). An analysis of transformations. Journal of the Royal Statistical Society Series B (Statistical Methodology), 26(2), 211–243.
[29]	Hyndman, R. J., & Athanasopoulos, G. (2021). Forecasting: Principles and Practice (3rd ed.). OTexts. https://otexts.com/fpp3/.
[30]	Hyndman, R.J., Athanasopoulos, G., Bergmeir, C., Caceres, G., Chhay, L., O'Hara-Wild, M., Petropoulos, F., Razbash, S., Wang, E., & Yasmeen, F. (2023). forecast: Forecasting functions for time series and linear models. R package version 8.21. https://pkg.robjhyndman.com/forecast/.
[31]	Hyndman, R.J. and Khandakar, Y. (2008) Automatic Time Series Forecasting: The Forecast Package for R. Journal of Statistical Software, 27(3), 1-22.
[32]	Ljung, G.M. and Box, G.E.P. (1978) On a Measure of a Lack of Fit in Time Series Models. Biometrika, 65(2), 297-303.
[33]	Akaike, H. (1974). A new look at the statistical model identification. IEEE Transactions on Automatic Control, 19(6), 716–723.
[34]	Schwarz, G. (1978) Estimating the Dimension of a Model. Annals of Statistics, 6(2), 461-464.
[35]	Makridakis, S. (1993). Accuracy measures: theoretical and practical concerns. International Journal of Forecasting, 9(4), 527–529.
[36]	Sailor, D., & Muñoz, J. R. (1997). Sensitivity of electricity and natural gas consumption to climate in the U.S.A.—Methodology and results for eight states. Energy, 22(10), 987–998.
[37]	Moral-Carcedo, J., & Vicéns-Otero, J. (2005). Modelling the non-linear response of Spanish electricity demand to temperature variations. Energy Economics, 27(3), 477–494.
[38]	Cleveland, W.S. (1993) Visualizing Data. Hobart Press, Summit.
[39]	Wei, W.W.S. (2006). Time Series Analysis, Univariate and Multivariate Methods. 2nd Edition, Pearson Addision Wesley, New York.
[40]	Burnham, K.P. and Anderson, D.R. (2002) Model Selection and Inference: A Practical Information-Theoretic Approach. 2nd Edition, Springer-Verlag, New York.