Forecast-Oriented Method of Complex Signal Ensemble Permutations Based on the ARIMA Model
DOI:
https://doi.org/10.31861/sisiot2025.2.02015Keywords:
telecommunication systems, optimization, complex signal ensembles, SNR, correlationAbstract
The article proposes a method for time-domain permutation of complex signal ensembles based on the Autoregressive Integrated Moving Average (ARIMA) model, referred to as ARIMA-permutation-based method. Unlike existing approaches, the method takes into account the temporal inertia of correlation variations, enabling real-time forecasting of ensemble dynamics and adaptive structural control under stochastic disturbances. The developed method and its implementation algorithm combine the ARIMA permutation-based method differencing operation with forecast-oriented selection of time-segment permutations, whose optimization is performed according to an integral criterion that considers correlation indicators, energy variation, and signal-to-noise ratio (SNR) stability. This integration ensures a balance between adaptability and convergence stability, allowing the forecast to rely on decorrelated signal increments rather than accumulated trends. Within the mathematical model, objective functions are formulated to describe the expected correlation, forecasting uncertainty, and energy consistency of the ensemble parameters. Minimization of integral criteria of ensemble configuration enables the selection of the optimal time-segment permutation and progressive refinement of the forecast during the iterative process. Experimental modeling was carried out for SNR values from 10 dB to 25 dB and time-segmentation parameters τ = 0.3 – 1.0, comparing three approaches: ARIMA-permutation-based method, the Markov model, and the LPT-τ permutation model. The results demonstrated a 20.2 % reduction in the mean absolute scaled error and a 15.3 % reduction in the mean scaled interval score compared with the Markov method, as well as an increase in residual stability by 47.1 % under signal fading conditions. It has been proven that the application of the ARIMA-permutation-based method effectively suppresses residual correlation, ensures short memory of differenced series, and improves the accuracy and robustness of forecasting under interference. The proposed approach can be applied to the optimization of signal formation and processing in cognitive telecommunication environments, particularly in the design of dynamic spectrum monitoring systems, distributed communication networks, and energy-efficient data transmission protocols.
Downloads
References
X. Zhang and W. Cao, “Research on time series forecasting method based on autoregressive integrated moving average model with zonotopic Kalman filter,” Sustainability, vol. 17, no. 7, p. 2993, 2025, https://www.mdpi.com/2071-1050/17/7/2993.
Q. Shi, J. Yin, J. Cai et al., “Block Hankel tensor ARIMA for multiple short time series forecasting,” 2002, doi: arXiv.2002.12135.
D. Bertsimas and L. Boussioux, “Ensemble modeling for time series forecasting: An adaptive robust optimization approach,” arXiv preprint arXiv:2304.04308, 2023, doi:10.48550/arXiv.2304.04308.
K. Perets, V. Lysechko, and O. Komar, “Modeling nonlinear signal components based on Volterra series in the frequency domain during spectral reconstruction,” Computer-Integrated Technologies: Education, Science, Production. Telecommunications and Radio Engineering, no. 57, pp. 192–201, 2024, doi:10.36910/6775-2524-0560-2024-57-23.
V. P. Lysechko, D. O. Kulagin, S. V. Indyk, O. S. Zhuchenko, and I. V. Kovtun, “The study of the cross-correlation properties of complex signals ensembles obtained by filtered frequency elements permutations,” Radio Electronics, Computer Science, Control, no. 2, pp. 15–23, 2022, doi: 10.15588/1607-3274-2022-2-2.
V. P. Lysechko, O. M. Komar, O. K. Veklych, and V. S. Bershov, “Optimization of the parameters of synthesized signals using linear approximations by the Nelder–Mead method,” Radio Electronics, Computer Science, Control, no. 3 (70), pp. 35–43, 2024, doi: 10.15588/1607-3274-2024-3-4.
S. A. Sherly, et al., “A hybrid approach to time series forecasting: Integrating ARIMA with deep learning,” Results in Engineering, 2025, doi: 10.1016/j.rineng.2025.105703.
M. A. Cruz-Nájera, “Short time series forecasting: Recommended methods and techniques,” Symmetry, vol. 14, no. 6, p. 1231, 2022, doi:10.3390/sym14061231.
N. S. Muruganandam, “Dynamic ensemble multivariate time series forecasting model for PM2.5,” Computer Systems Science and Engineering, vol. 44, no. 2, 2023, doi:10.32604/csse.2023.024943.
I. A. Ibrahim et al., “Short-term multivariate time series load data forecasting at individual and aggregate load levels,” Energy Conversion and Management, vol. 296, p. 117663, Nov. 2023, doi:10.1016/j.enconman.2023.117663.
G. Çınarer et al., “Hybrid deep learning and stacking ensemble model for time series forecasting,” Electronics, vol. 14, no. 16, p. 3213, 2025, doi;10.3390/electronics14163213.
J. Kim et al., “A comprehensive survey of deep learning for time series forecasting: Architectural diversity and open challenges,” Artificial Intelligence Review, vol. 58, p. 216, 2025, doi:10.1007/s10462-025-11223-9.
K. W. Ng et al., “Experimental evaluation of baselines for forecasting social dynamics: An ensemble ARIMA + Hawkes approach,” EPJ Data Science, 2023, doi:10.1140/epjds/s13688-023-00383-9.
J. Garland, R. James, and E. Bradley, “Model-free quantification of time-series predictability,” Physical Review E, vol. 90, p. 052910, 2014, doi;10.1103/PhysRevE.90.052910.
G. Xie, T. Ren, and Y. Yang, “A novel decomposed-ensemble time series forecasting framework,” arXiv preprint arXiv:2310.08812, 2023, doi: arxiv.org/html/2310.08812.
Published
Issue
Section
License
Copyright (c) 2025 Security of Infocommunication Systems and Internet of Things
This work is licensed under a Creative Commons Attribution 4.0 International License.
