Dynamic Modeling of Energy Data: World Crude Oil and Coal Prices 2017-2023 (A State-Space Model Analysis of Multivariate Time Series)
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Keywords:
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Unit Root Test, VAR(p) Model, Granger-Causality, State Space Model, Forecasting
Abstract
The analysis of global crude oil and coal prices has attracted considerable research interest, as these prices significantly affect both society and industry, making the topic highly relevant for governments and policy makers. This study examines the correlation between global coal and crude oil prices from 2017 to 2023. It analyzes the behavior of these price series using a unit root test and develops an optimal model for conducting a Granger-causality analysis. To forecast crude oil and coal prices for the next 30 periods, a state-space modeling approach is applied. The unit root test results reveal that these prices are non-stationary, suggesting that any shocks to prices will have persistent effects. The best-fitting model for the association between coal and crude oil prices is a vector autoregressive model of order two (VAR(2)). The Granger-causality results reveal that current crude oil prices are influenced by both their own past values and previous coal prices, and vice versa. Forecasts using the state-space model suggest a modest upward trend for crude oil prices over the next 30 periods, while coal prices are projected to rise more strongly.
References
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Heiss, F. (2008). Sequential Numerical Integration in Nonlinear State Space Models for Microeconometric Panel Data. Journal of Applied Econometrics, 23; 373–389
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Russel, E., W. Wamiliana, W. Warsono, N. Nairobi, M. Usman, and F. A. M. Elfaki (2023). AnalysisMultivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia. Science and Technology Indonesia, 8(1); 144–150
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Smith, M. S. andW. Maneesoonthorn (2018). Inversion Copulas from Nonlinear State SpaceModels with an Application to Inflation Forecasting. International Journal of Forecasting, 34; 389–407
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Usman, M., M. Komaruddin, M. Sarida, W. Wamiliana, E. Russel, M. Kufepaksi, I. A. Alam, and F. A. M. Elfaki (2022). Analysis of Some Variable Energy Companies by Using VAR(p)-GARCH(r,s) Model: Study From Energy Companies of Qatar Over the Years 2015–2022. International Journal of Energy Economics and Policy, 12(5); 178–191
Virginia, E., J. Ginting, and F. A. M. Elfaki (2018). Application of GARCH Model to Forecast Data and Volatility of Share Price of Energy (Study on Adaro Energy Tbk, LQ45). International Journal of Energy Economics and Policy, 8(3); 131–140
Warsono, W., E. Russel, A. R. Putri, W. Wamiliana, W. Widiarti, and M. Usman (2020). Dynamic Modeling Using Vector Error-Correction Model: Studying the Relationship Among Data Share Price of Energy PGAS Malaysia, AKRA, Indonesia, and PTT PCL-Thailand. International Journal of Energy Economics and Policy, 10(2); 360–373
Warsono, W., E. Russel, W. Wamiliana, W. Widiarti, and M. Usman (2019a). Vector Autoregressive with Exogenous Variable Model and Its Application in Modeling and Forecasting Energy Data: Case Study of PTBA and HRUM Energy. International Journal of Energy Economics and Policy, 9(2); 390–398
Warsono, W., E. Russel, W. Wamiliana, W. Widiarti, and M. Usman (2019b). Modeling and Forecasting by the Vector Autoregressive Moving Average Model for Export of Coal and Oil Data (Case Study from Indonesia Over the Years 2002-2017). International Journal of Energy Economics and Policy, 9(4); 240–247
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Wei, W. W. S. (2019). Multivariate Time Series Analysis and Application. JohnWiley and Sons, New York
Weiqi, L., M. Linwei, D. Yaping, and L. Donghai (2012). Short-Term Oil Price Forecasting Based on State Space Model. Advanced Materials Research, 403-408; 2530–2534
Welch, G., G. Bishop, L. Vicci, S. Brumback, K. Keller, and D. Colucci (2001). High-PerformanceWide-Area Optical Tracking: The Hiball Tracking System. Presence, 10(1); 1–21
West, M. and J. Harrison (1997). Bayesian Forecasting and Dynamic Models. 2nd Edition. Springer, Berlin, Heidelberg
Aoki, M. (1987). State Space Modelling of Time Series. Springer-Verlag, Berlin
Aoki, M. (1994). Modeling Economic Time Series by Forward and Backward State Space Innovation Models and IV Estimators. European Journal of Operational Research, 73; 265–278
Basu, S., X. Li, and G. Michailidis (2019). Low Rank and Structured Modeling of High-Dimensional Vector Autoregressions. IEEE Transactions on Signal Processing, 67(5); 1207–1222
Brockwell, P. J. and R. A. Davis (1991). Time Series: Theory and Methods. Springer-Verlag, New York
Commandeur, J. J. F. and S. J. Koopman (2007). An Introduction to State Space Time Series Analysis. Oxford University Press, New York
Diebold, F. X. (1989). State Space Modeling of Time Series: A Review Essay. Journal of Economic Dynamics and Control, 13; 597–612
Durbin, J. and S. J. Koopman (2012). Time Series Analysis by State Space Methods. Oxford University Press, Oxford, 2nd edition
Enders, W. (2015). Applied Econometric Time Series. John Wiley and Sons Interscience Publication, USA, 4th edition
Florens, J. P., V. Marimoutou, and A. P. Feissolle (2007). Econometric Modeling and Inference. Oxford University Press, New York
Gomez, V. (2016). Multivariate Time Series with Linear State Space Structure. Springer, New York
Gu, A. and T. Dao (2023). Mamba: Linear-Time Sequence Modeling with Selective State Spaces. arXiv preprint arXiv, 2312; 00752
Gu, A., K. Goel, A. Gupta, and C. Ré (2022). On the Parameterization and Initialization of Diagonal State Space Models. NeurIPS, 35; 35971–35983
Gu, A., K. Goel, and C. Re (2021). Efficiently Modeling Long Sequences with Structured State Spaces. In ICLR
Hagiwara, J. (2021). Time Series Analysis for the State-Space Model with R/Stan. Springer Nature Singapore Pte Ltd
Hamilton, H. (1994). Time Series Analysis. Princeton University Press, Princeton, New Jersey
Hannan, E. J. and M. Deistler (1988). The Statistical Theory of Linear Systems. John Wiley, New York
Harvey, A. C. (2009). Forecasting, Structural Time Series Models and the Kalman Filter. Cambridge University Press, Cambridge
Heiss, F. (2008). Sequential Numerical Integration in Nonlinear State Space Models for Microeconometric Panel Data. Journal of Applied Econometrics, 23; 373–389
Hu, Z., J. Ma, L. Yang, L. Yao, and M. Pang (2019). Monthly Electricity Demand Forecasting Using Empirical Mode Decomposition-Based State Space Model. Energy & Environment, 0(0); 1–19
Kalman, R. E. (1960). A New Approach to Linear Filtering and Prediction Problems. Transaction of American Society Mechanical Engineering Journal of Basic Engineering, 83D; 35–45
Kalman, R. E. and R. S. Bucy (1961). New Results in Linear Filtering and Prediction Theory. Transaction of American Society Mechanical Engineering Journal of Basic Engineering, 83; 95–108
Kilian, L. and H. Lutkepohl (2019). Structural Vector Autoregressive Analysis. Cambridge University Press
Kurniasari, D., T. P. Shella, M. Usman, and W. Warsono (2025). A Hybrid ARIMA–GRU Model for Forecasting Palm Oil Prices at PT Sawit Sumbermas Sarana in Central Kalimantan. Integra: Journal of Integrated Mathematics and Computer Science, 2(1); 7–14
Kurniati, D., A. Hoyyi, and T. Widiharih (2019). State Space Model Approach for Forecasting the Use of Electrical Energy (a Case Study On: PT. PLN (Persero) District of Kroya). In IOP Conf. Series: Journal of Physics: Conf. Series, volume 1025. page 012109
Lin, J. and G. Michailidis (2024). Deep Learning-Based Approaches for State Space Models: A Selective Review. arXiv preprint arXiv:2412.11211
Lutkepohl, H. (2005). New Introduction to Multiple Time Series Analysis. Springer-Verlag, Berlin
Madsen, H. (2008). Time Series Analysis. Chapman & Hall/CRC, New York
Nagbe, K., J. Cugliari, and J. Jacques (2018). Short Term Electricity Demand Forecasting Using a Functional State Space Model. Energies, 11; 1120
Pandher, G. S. (2002). Forecasting Multivariate Time Series with Linear Restrictions Using Constrained Structural State-Space Models. J. Forecast., 21; 281–300
Pao, H. T. (2009). Forecast of Electricity Consumption and Economic Growth in Taiwan by State Space Modeling. Energy, 34; 1779–1791
Parreno, S. J. E. (2024). Assessing the Stationarity of Per Capita Electricity Consumption: Time Series Analysis in ASEAN Countries. International Journal of Energy Economics and Policy, 14(2); 46–52
Pena, D., G. C. Tiao, and R. S. Tsay (2001). A Course in Time Series Analysis. John Wiley and Sons, New York
Prado, R. and M. West (2010). Time Series: Modeling, Computation, and Inference. CRC Press, New York
Ramos, P., N. Santos, and R. Rebelo (2015). Performance of State Space and ARIMA Models for Consumer Retail Sales Forecasting. Robotics and Computer Integrated Manufacturing, 34; 151–163
Rangapuram, S. S., M. Seeger, J. Gasthaus, S.W. Lorenzo, and T. Januschowski (2018). Deep State Space Models for Time Series Forecasting. In 32nd Conference on Neural Information Processing Systems (NeurIPS 2018). Montreal, Canada, pages 1–10
Russel, E., W. Wamiliana, W. Warsono, N. Nairobi, M. Usman, and F. A. M. Elfaki (2023). AnalysisMultivariate Time Series Using State Space Model for Forecasting Inflation in Some Sectors of Economy in Indonesia. Science and Technology Indonesia, 8(1); 144–150
Sanchez-Bornot, J. M. and R. C. Sotero (2023). Machine Learning for Time Series Forecasting Using State Space Models. In P. Quaresma, D. Camacho, H. Yin, T. Gonçalves, V. Julian, and A. J. Tallón-Ballesteros, editors, IntelligentData Engineering and Automated Learning – IDEAL 2023, volume 14404 of Lecture Notes in Computer Science. Springer, Cham
Sari, D. R., D. E. N.Widiarti, M. Usman, and L. Love (2024). Application of GSTARMA Spatial-Temporal Model for Inflation Analysis in South Sulawesi Province. Integra: Journal of Integrated Mathematics and Computer Science, 1(3); 87–96
Sims, C. A. (1980). Macroeconomics and Reality. Econometrica, 48(1); 1–48
Siontis, K. C., P. A.Noseworthy, Z. I. Attia, and P. A. Friedman (2021). Artificial Intelligence-Enhanced Electrocardiography in Cardiovascular Disease Management. Nature Reviews Cardiology, 18(7); 465–478
Smith, M. S. andW. Maneesoonthorn (2018). Inversion Copulas from Nonlinear State SpaceModels with an Application to Inflation Forecasting. International Journal of Forecasting, 34; 389–407
Snyder, R. D., J. K. Ord, A. B. Koehler, K. R. McLaren, and A. N. Beaumont (2017). Forecasting Compositional Time Series: A State Space Approach. International Journal of Forecasting, 33; 502–512
Tsay, R. S. (2010). Analysis of Financial Time Series. JohnWiley & Sons, Inc., New York
Tsay, R. S. (2014). Multivariate Time Series Analysis. JohnWiley and Sons, New York
Usman, M., M. Komaruddin, M. Sarida, W. Wamiliana, E. Russel, M. Kufepaksi, I. A. Alam, and F. A. M. Elfaki (2022). Analysis of Some Variable Energy Companies by Using VAR(p)-GARCH(r,s) Model: Study From Energy Companies of Qatar Over the Years 2015–2022. International Journal of Energy Economics and Policy, 12(5); 178–191
Virginia, E., J. Ginting, and F. A. M. Elfaki (2018). Application of GARCH Model to Forecast Data and Volatility of Share Price of Energy (Study on Adaro Energy Tbk, LQ45). International Journal of Energy Economics and Policy, 8(3); 131–140
Warsono, W., E. Russel, A. R. Putri, W. Wamiliana, W. Widiarti, and M. Usman (2020). Dynamic Modeling Using Vector Error-Correction Model: Studying the Relationship Among Data Share Price of Energy PGAS Malaysia, AKRA, Indonesia, and PTT PCL-Thailand. International Journal of Energy Economics and Policy, 10(2); 360–373
Warsono, W., E. Russel, W. Wamiliana, W. Widiarti, and M. Usman (2019a). Vector Autoregressive with Exogenous Variable Model and Its Application in Modeling and Forecasting Energy Data: Case Study of PTBA and HRUM Energy. International Journal of Energy Economics and Policy, 9(2); 390–398
Warsono, W., E. Russel, W. Wamiliana, W. Widiarti, and M. Usman (2019b). Modeling and Forecasting by the Vector Autoregressive Moving Average Model for Export of Coal and Oil Data (Case Study from Indonesia Over the Years 2002-2017). International Journal of Energy Economics and Policy, 9(4); 240–247
Wei, W. W. S. (2006). Time Series Analysis: Univariate and Multivariate Methods. Addison-Wesley Publishing Company, Redwood City, California
Wei, W. W. S. (2019). Multivariate Time Series Analysis and Application. JohnWiley and Sons, New York
Weiqi, L., M. Linwei, D. Yaping, and L. Donghai (2012). Short-Term Oil Price Forecasting Based on State Space Model. Advanced Materials Research, 403-408; 2530–2534
Welch, G., G. Bishop, L. Vicci, S. Brumback, K. Keller, and D. Colucci (2001). High-PerformanceWide-Area Optical Tracking: The Hiball Tracking System. Presence, 10(1); 1–21
West, M. and J. Harrison (1997). Bayesian Forecasting and Dynamic Models. 2nd Edition. Springer, Berlin, Heidelberg
Authors
Russel, E., Wamiliana, Usman, M., Elfaki, F. A., Adnan, A., & Lindrianasari. (2025). Dynamic Modeling of Energy Data: World Crude Oil and Coal Prices 2017-2023 (A State-Space Model Analysis of Multivariate Time Series). Science and Technology Indonesia, 10(4), 1301–1311. https://doi.org/10.26554/sti.2025.10.4.1301-1311
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