Forecasting early warning signals for abrupt transitions in oil systems: A deep learning-based network and regime switching model

Abstract

Abrupt transitions that are associated with global crisis events can lead to systemic collapse. Previous models for investigating early warning signals for time series–based oil systems focused on the fluctuation characteristics of single points and ignored the dynamic process in the oil series, which is characterized both by historical changes in the oil series and by its nonlinear fluctuations coupled with related variables. In this study, an early warning model that combines a deep learning model, a Markov regime-switching model and a reconstructed hybrid network, including a self-dynamic network and a relationship-dynamic network, is proposed. West Texas Intermediate (WTI) crude oil and natural gas futures daily prices are selected as the sample data. Abrupt transitions are identified, and their characteristics that are influenced by typical events are investigated. The dynamic features can be measured through the structures of the hybrid network; the in-degrees, out-degrees, and weighted degrees of the nodes follow power-law distributions. Early warning signals for abrupt transitions can be effectively captured via the deep learning model. Importantly, the deep learning-based early warning model integrated with the hybrid network outperforms that integrated with the self-dynamic network, with the average accuracies of both models on the training and testing sets exceeding 90%. This work contributes to energy management research and provides early warning tools for policymakers and market investors.

Graphical abstract

Keywords

complex network time series / deep learning / early warning signals / abrupt transition / oil system / crude oil / natural gas

References

[1] An S, An F, Gao X, Wang A, (2023). Early warning of critical transitions in crude oil price. Energy, 280: 128089

[2] Antonakakis N, Cunado J, Filis G, Gabauer D, de Gracia F P, (2023). Dynamic connectedness among the implied volatilities of oil prices and financial assets: New evidence of the COVID-19 pandemic. International Review of Economics & Finance, 83: 114–123

[3] Atil A, Lahiani A, Nguyen D K, (2014). Asymmetric and nonlinear pass-through of crude oil prices to gasoline and natural gas prices. Energy Policy, 65: 567–573

[4] Benkraiem R, El-Khatib Y, Fan J, Goutte S, Klein T, (2025). Optimal risk management considering environmental and climatic changes. Risk Analysis, 45( 3): 544–562

[5] Bian S, Wang Z, Leng S, Lin W, Shi J, (2025). Utilizing causal network markers to identify tipping points ahead of critical transition. Advanced Science, 12( 42): e15732

[6] Chen P, Suo Y, Aihara K, Li Y, Wu D, Liu R, Chen L J A S, (2025). Ultralow-dimensionality reduction for identifying critical transitions by spatial-temporal PCA. Advanced Science, 12: 2408173

[7] Dai Z, Zhu H, (2022). Time-varying spillover effects and investment strategies between WTI crude oil, natural gas and Chinese stock markets related to belt and road initiative. Energy Economics, 108: 105883

[8] Dang W, Lv D, Jing F, Yu P, Guo W, Gao Z, (2024). A novel multiphase flow water cut modeling framework based on flow behavior-heuristic deep learning. Engineering Applications of Artificial Intelligence, 136: 108956

[9] de Castro Matias M, Tabak B M, (2025). Comparison of indicator saturation and Markov regime-switching models for Brazilian electricity prices. Energy Economics, 144: 108341

[10] Doornik J A, (2013). A Markov-switching model with component structure for US GNP. Economics Letters, 118( 2): 265–268

[11] Feng Q, Wu Q, Hai X, Ren Y, Wen C, Wang Z, (2025). Deep reinforcement learning-based resilience optimization for infrastructure networks restoration with multiple crews. Frontiers of Engineering Management, 12( 1): 141–153

[12] Gatfaoui H, de Peretti P, (2019). Flickering in information spreading precedes critical transitions in financial markets. Scientific Reports, 9( 1): 5671

[13] Geng J, Ji Q, Fan Y, (2017). The relationship between regional natural gas markets and crude oil markets from a multi-scale nonlinear Granger causality perspective. Energy Economics, 67: 98–110

[14] Gross B, Volotsenko I, Sallem Y, Yadid N, Bonamassa I, Havlin S, Frydman A, (2025). The random cascading origin of abrupt transitions in interdependent systems. Nature Communications, 16( 1): 5869

[15] Guttal V, Raghavendra S, Goel N, Hoarau Q, (2016). Lack of critical slowing down suggests that financial meltdowns are not critical transitions, yet rising variability could signal systemic risk. PLoS One, 11( 1): e0144198

[16] Hasanli M, (2024). Re-examining crude oil and natural gas price relationship: Evidence from time-varying regime-switching models. Energy Economics, 133: 107510

[17] Hellmann F, Schultz P, Jaros P, Levchenko R, Kapitaniak T, Kurths J, Maistrenko Y, (2020). Network-induced multistability through lossy coupling and exotic solitary states. Nature Communications, 11( 1): 592

[18] Horváth L, Trapani L, Wang S, (2025). Sequential monitoring for changes in GARCH (1, 1) models without assuming stationarity. Journal of Time Series Analysis, 46( 5): 981–1023

[19] Jian Z, Li X, (2021). Skewness-based market integration: A systemic risk measure across international equity markets. International Review of Financial Analysis, 74: 101664

[20] Kim C J, Nelson C R, (2017). State-space models with regime switching: Classical and Gibbs-sampling approaches with applications.

[21] Kumar A, Mallick S, (2024). Oil price dynamics in times of uncertainty: Revisiting the role of demand and supply shocks. Energy Economics, 129: 107152

[22] Li X, Ghosh D, Lei Y, Small M, (2025). Synchronization and chimera states in time-varying multilayer networks with higher-order interactions. Chaos. 35( 5): 053148

[23] Lin X, Meng Y, Zhu H, (2024). Exploring hedging potentials of green bonds against oil price shocks: Evidence from quantile-on-quantile connectedness measures. Finance Research Letters, 65: 105640

[24] Mari C, Mari E, (2023). Deep learning based regime-switching models of energy commodity prices. Energy Systems, 14( 4): 913–934

[25] Masuda N, Aihara K, MacLaren N G, (2024). Anticipating regime shifts by mixing early warning signals from different nodes. Nature Communications, 15( 1): 1086

[26] Menardi G, Torelli N, (2014). Training and assessing classification rules with imbalanced data. Data Mining and Knowledge Discovery, 28( 1): 92–122

[27] Mignon V, Saadaoui J, (2024). How do political tensions and geopolitical risks impact oil prices. Energy Economics, 129: 107219

[28] Nelson D B, (1990). Stationarity and persistence in the GARCH(1, 1) model. Econometric Theory, 6( 3): 318–334

[29] O’Brien D A, Deb S, Gal G, Thackeray S J, Dutta P S, Matsuzaki S S, May L, Clements C F, (2023). Early warning signals have limited applicability to empirical lake data. Nature Communications, 14( 1): 7942

[30] Peng H, Chen P, Yang N, Aihara K, Liu R, Chen LJNSR, (2025). One-core neuron deep learning for time series prediction. National Science Review, 12( 2): nwae441

[31] Qiu Y, Sun X, Xiong X, Si S, (2025). Systemic financial risk analysis of the US based on the complex network. Journal of Management Science and Engineering, 10( 3): 414–433

[32] Rietkerk M, Skiba V, Weinans E, Hébert R, Laepple T, (2025). Ambiguity of early warning signals for climate tipping points. Nature Climate Change, 15: 479–488

[33] Rye C D, Jackson T, (2020). Using critical slowing down indicators to understand economic growth rate variability and secular stagnation. Scientific Reports, 10( 1): 10481

[34] Scheffer M, (2010). Foreseeing tipping points. Nature, 467( 7314): 411–412

[35] Scheffer M, Bascompte J, Brock W A, Brovkin V, Carpenter S R, Dakos V, Held H, Van Nes E H, Rietkerk M, Sugihara G, (2009). Early-warning signals for critical transitions. Nature, 461( 7260): 53–59

[36] Segnon M, Gupta R, Wilfling B, (2024). Forecasting stock market volatility with regime-switching GARCH-MIDAS: The role of geopolitical risks. International Journal of Forecasting, 40( 1): 29–43

[37] Shen J, Chen N, Niu B, Zhong J, Liu R, (2025). FatePredictor: Cell fate decision-making prediction with an ensemble deep learning model. The Innovation, 6( 11): 101010

[38] Song S, Li H, (2024). Early warning signals for stock market crashes: empirical and analytical insights utilizing nonlinear methods. EPJ Data Science, 13( 1): 16

[39] Tiwari A K, Jena S K, Kumar S, Hille E, (2022). Is oil price risk systemic to sectoral equity markets of an oil importing country? Evidence from a dependence-switching copula delta CoVaR approach. Annals of Operations Research, 315( 1): 429–461

[40] Wang M, Zhao L, Du R, Wang C, Chen L, Tian L, Eugene Stanley H., (2018). A novel hybrid method of forecasting crude oil prices using complex network science and artificial intelligence algorithms. Applied Energy, 220: 480–495

[41] Wang Y, Ding X, Wang P, Huang Z, (2024). Impact of global crisis events on the dependence and risk spillover between gold and crude oil: A regime-switching copula approach. Humanities & Social Sciences Communications, 11: 1751

[42] Wang Z, Dong Z, (2024). Volatility spillover effects among geopolitical risks and international and Chinese crude oil markets——A study utilizing time-varying networks. Resources Policy, 96: 105225

[43] Widodo A, Shim M C, Caesarendra W, Yang B S, (2011). Intelligent prognostics for battery health monitoring based on sample entropy. Expert Systems with Applications, 38( 9): 11763–11769

[44] Wu H, Li P, Cao J, Xu Z, (2024). Forecasting the Chinese crude oil futures volatility using jump intensity and Markov-regime switching model. Energy Economics, 134: 107588

[45] Yan Q, Owen L A, Wei T, Hughes P D, Kong X, Jiang N, Zhang J, Zhang Z, Wang H, (2025). Regime shift to extensive valley glaciations over High Mountain Asia during the Early-Middle Pleistocene. Nature Communications, 16( 1): 5185

[46] Yu R, Wang R, (2024). Learning dynamical systems from data: An introduction to physics-guided deep learning. Proceedings of the National Academy of Sciences of the United States of America, 121( 27): e2311808121

[47] Zhang H, Hong H, Ding S, (2023). The role of climate policy uncertainty on the long-term correlation between crude oil and clean energy. Energy, 284: 128529

[48] Zhang Y, Zhang L, (2015). Interpreting the crude oil price movements: Evidence from the Markov regime switching model. Applied Energy, 143: 96–109

[49] Zhen Z, Tian L, Lu J, (2019). Analysis of oil prices’ interaction in the USA based on complex networks. Energy Sources. Part B, Economics, Planning, and Policy, 14( 1): 1–12

[50] Zhi W, Appling A P, Golden H E, Podgorski J, Li L, (2024). Deep learning for water quality. Nature Water, 2( 3): 228–241

[51] Zhong H, Ding J, Lei Y, Small M, (2025). Taming chimeras in multiplex networks of coupled oscillators based on multi-agent deep reinforcement learning. Physica A, 680: 131026

RIGHTS & PERMISSIONS

Higher Education Press