Robustness Evaluation of ANFIS, Hybrid GA-SVM, and SVM under Controlled Time Series Structures
Abstract
This study evaluates the robustness of ANFIS, hybrid GA-SVM, and SVM under synthetic time-series structures using a factorial simulation framework combined with empirical validation. From a practical perspective, robust coal price forecasting is essential for supporting energy planning, trade management, and policy decision-making under uncertain market conditions. Empirical analysis of Indonesian coal prices reveals nonstationary behaviour, high volatility, and nonlinear dynamics. Forecasting performance is assessed using walk-forward validation, where SVM and hybrid GA-SVM demonstrate comparable accuracy and outperform ANFIS on the empirical dataset. To systematically examine model sensitivity to structural variations, a factorial simulation design is implemented by varying seasonality, volatility, and predictor–response structure across 12 scenarios with 100 replications each. The results indicate that volatility is the most dominant factor affecting forecasting error, with significant interaction effects among structural factors. ANOVA and post hoc analysis further confirm that model performance depends more on data characteristics than on algorithmic complexity. These findings demonstrate that factorial simulation provides a systematic and robust framework for evaluating forecasting models beyond conventional empirical comparisons, while offering deeper insight into the relationship between data structure and model performance.
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B. Wu, D. Huang, and M. Chen, “Estimating contagion mechanism in global equity market with time-zone effect,” Financ. Manag., vol. 52, no. 3, pp. 543–572, 2023, doi: 10.1111/fima.12430.
G. Palomba and M. Tedeschi, “Geopolitical Risks’ Spillovers Across Countries and on Commodity Markets: A Dynamic Analysis,” Energy Res. Lett., vol. 6, no. 2, pp. 1–8, 2025, doi: 10.46557/001c.121262.
J. D. Hamilton, Time Series Analysis. Princeton, New Jersey, USA: Princeton University Press, 1994. doi: 10.2307/j.ctv14jx6sm.
A. Almeida, S. Brás, S. Sargento, and F. C. Pinto, “Time series big data: a survey on data stream frameworks, analysis and algorithms,” J. Big Data, vol. 10, no. 1, p. 83, May 2023, doi: 10.1186/s40537-023-00760-1.
B. Nguyen-Thai, V. Le, N. D. T. Tieu, T. Tran, S. Venkatesh, and N. Ramzan, “Learning evolving relations for multivariate time series forecasting,” Appl. Intell., vol. 54, no. 5, pp. 3918–3932, 2024, doi: 10.1007/s10489-023-05220-0.
S. C. Huang and R. S. Tsay, “Time Series Forecasting with Many Predictors,” Mathematics, vol. 12, no. 15, 2024, doi: 10.3390/math12152336.
J. S. R. Jang, “ANFIS: Adaptive-Network-Based Fuzzy Inference System,” IEEE Trans. Syst. Man Cybern., vol. 23, no. 3, pp. 665–685, 1993, doi: 10.1109/21.256541.
V. Vapnik, The Nature of Statistical Learning Theory, Second Edition, 2nd ed. New York Inc: Springer Berlin Heidelberg, 1995.
C. Cortes and V. Vapnik, “Support-Vector Networks,” Mach. Learn., vol. 20, pp. 273–297, 1995, doi: 10.1007/BF00994018.
B. Schölkopf and A. J. Smola, Learning With Kernels: Support Vector Machines, Regularization, Optimization, and Beyond. Cambridge, MA, USA: MIT Press, 2002.
D. E. Goldberg, Genetic algorithms in optimization, search and machine learning, 1st editio. Reading, MA, USA: Addison-Wesley Publishing Company, 1989. [Online]. Available: https;//books.google.co.id/books?
R. L. Haupt, S. E. Haupt, and A. J. Wiley, Pratical Genetic Algorithms, 2nd ed. Hoboken New Jersey: John Wiley & Sons, 2004.
Z. Alameer, M. A. Elaziz, A. A. Ewees, H. Ye, and Z. Jianhua, “Forecasting Copper Prices Using Hybrid Adaptive Neuro-Fuzzy Inference System and Genetic Algorithms,” Nat. Resour. Res., vol. 28, no. 4, pp. 1385–1401, 2019, doi: 10.1007/s11053-019-09473-w.
P. Hendikawati, Subanar, Abdurakhman, and Tarno, “ANFIS Performance Evaluation for Predicting Time Series with Calendar Effects,” IAENG Int. J. Appl. Math., vol. 51, no. 3, pp. 1–12, 2021, [Online]. Available: https://www.iaeng.org/IJAM/issues_v51/issue_3/index.html.
M. . Alquraish, K. . Abuhasel, A. . Alqahtani, and M. A. Khadr, “Comparative Analysis of Hidden Markov Model, Hybrid Support Vector Machines, and Hybrid Artificial Neural Fuzzy Inference System in Reservoir Inflow Forecasting (Case Study: The King Fahd Dam, Saudi Arabia).,” Water, vol. 13, no. 1236, 2021, doi: doi.org/10.3390/w13091236.
Ö. Öztunç Kaymak and Y. Kaymak, “Prediction of crude oil prices in COVID-19 outbreak using real data,” Chaos, Solitons and Fractals, vol. 158, 2022, doi: 10.1016/j.chaos.2022.111990.
A. V. Sinaga, N. C. Biutarbutar, T. B. Simamora, and J. Amalia, “Adaptive Neuro Fuzzy Inference System Optimization by Genetic Algorithm pada Time Series,” DoubleClick J. Comput. Inf. Technol., vol. 6, no. 1, pp. 25–31, 2022, doi: 10.25273/doubleclick.v6i1.13368.
S. Oladipo and Y. Sun, “Enhanced adaptive neuro ‑ fuzzy inference system using genetic algorithm : a case study in predicting electricity consumption,” SN Appl. Sci., vol. 5, no. 6, p. 186, 2023, doi: 10.1007/s42452-023-05406-8.
M. S. Bakare, A. Abdulkarim, A. N. Shuaibu, and M. M. Muhamad, “A hybrid long-term industrial electrical load forecasting model using optimized ANFIS with gene expression programming,” Energy Reports, vol. 11, no. May, pp. 5831–5844, 2024, doi: 10.1016/j.egyr.2024.05.045.
K. Drachal and M. Pawłowski, “A Review of the Applications of Genetic Algorithms to Forecasting Prices of Commodities.,” Economies, vol. 9, p. 6, 2021, doi: 10.3390/economies9010006.
R. Nayan, V. Rahul, D. Rakesh, N. Subbarao, and G. Pratap, “A new fuzzy support vector machine with pinball loss,” Discov. Artif. Intell., vol. 3, no. March, p. 14, 2023, doi: 10.1007/s44163-023-00057-5.
D. Ullmann, O. Taran, and S. Voloshynovskiy, “Multivariate Time Series Information Bottleneck,” Entropy, vol. 25, no. 5, p. 831, 2023, doi: 10.3390/e25050831.
M. Cheng, Q. Liu, Z. Liu, Z. Li, Y. Luo, and E. Chen, FormerTime: Hierarchical Multi-Scale Representations for Multivariate Time Series Classification, vol. 1, no. 1. Association for Computing Machinery, 2023. doi: 10.1145/3543507.3583205.
M. Cheng et al., “TimeMAE: Self-Supervised Representations of Time Series with Decoupled Masked Autoencoders,” Proc. Ninet. ACM Int. Conf. Web Search Data Min. (WSDM ’26), Febr. 22-26, 2026, Boise, ID, USA, vol. 1, no. 1, pp. 498–508, 2026, doi: 10.1145/3773966.3778007.
C.-M. Lin and Y.-S. Lin, “TPTM-HANN-GA: A Novel Hyperparameter Optimization Framework Integrating the Taguchi Method, an Artificial Neural Network, and a Genetic Algorithm for the Precise Prediction of Cardiovascular Disease Risk,” Mathematics, vol. 12, no. 1303, p. 9, 2024, doi: 10.3390/math12091303.
M. Hamoudia and S. and E. S. Makridakis, Forecasting with artificial intelligence Theory and Artificial, 1st ed. Switzerland: Palgrave Macmillan Cham, 2023. doi: 10.1007/978-3-031-35879-1.
J. Kim, H. Kim, H. G. Kim, D. Lee, and S. Yoon, “A comprehensive survey of deep learning for time series forecasting: architectural diversity and open challenges,” Artif. Intell. Rev., vol. 58, no. 7, p. 216, 2025, doi: 10.1007/s10462-025-11223-9.
S. S. W. Fatima and A. Rahimi, “A Review of Time-Series Forecasting Algorithms for Industrial Manufacturing Systems,” Machines, vol. 12, no. 6, p. 380, 2024, doi: 10.3390/machines12060380.
M. Bishop,C, Pattern Recognition and Machine Learning. New York, USA: Springer US, 2006. doi: 10.53759/7669/jmc202404020.
C. Bergmeir and J. M. Benítez, “On the use of cross-validation for time series predictor evaluation,” Inf. Sci. (Ny)., vol. 191, pp. 192–213, 2012, doi: 10.1016/j.ins.2011.12.028.
R. J. Hyndman and George Athanasopoulos, Forecasting: Principles and Practice, 2nd ed. Australia: OTexts, 2018.
F. X. Diebold and R. S. Mariano, “Comparing predictive accuracy,” J. Bus. Econ. Stat., vol. 13, no. 3, pp. 253–263, 1995, doi: 10.1080/07350015.1995.10524599.
S. Makridakis, S. C. Wheelwright, and R. J. Hyndman, Forecasting: Methods and Applications, 3rd Editio. New York, NY, USA: John Wiley & Sons, 1998.
R. J. Hyndman and A. B. Koehler, “Another look at measures of forecast accuracy,” Int. J. Forecast., vol. 22, no. 4, pp. 679–688, 2006, doi: 10.1016/j.ijforecast.2006.03.001.
T. Chai and R. R. Draxler, “Root mean square error (RMSE) or mean absolute error (MAE)? -Arguments against avoiding RMSE in the literature,” Geosci. Model Dev., vol. 7, no. 3, pp. 1247–1250, 2014, doi: 10.5194/gmd-7-1247-2014.
D. C. Montgomery, Design and Analysis of Experiment, 9th ed. Hoboken New Jersey: John Wiley & Sons, 2017.
DOI: http://dx.doi.org/10.30829/zero.v10i1.29313
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