面向长期时间序列预测的多项式投影与信息交换架构

doi:10.3778/j.issn.1002-8331.2401-0193

摘要/Abstract

摘要： 长期时间序列预测利用历史数据对未来较远时段的序列走势进行预测，为长期预警、规划和决策提供支持。现有方法在进行长期预测时，普遍存在分布偏移和长期依赖关系难以捕获的问题。提出一种面向长期时间序列预测的多项式投影与信息交换架构LPPIEA（Legendre polynomial projection and information exchange architecture）。引入可逆实例数据归一化，降低长期时间序列中分布偏移对预测的影响。使用勒让德多项式投影来处理复杂的时间模式，获取数据的高维特征表示以增强模型推理长期时间序列的能力。为了有效捕获长期时间依赖关系，构建轻量化的信息交换架构来高效捕获长期时间依赖关系，从而实现准确高效的长期时间序列预测。在4个常用的公开数据集上的实验结果表明，LPPIEA的预测误差相比于基线方法平均降低11.4%，同时还具有较高的计算效率。

关键词: 时间序列预测, 长期时间依赖, 多项式投影, 信息交换架构, 深度学习

Abstract: Long-term time series forecasting utilizes historical data to predict the trends of future sequences over extended periods, providing support for long-term warning, planning, and decision-making. Existing methods commonly encounter issues of distribution shifts and long-term dependencies that are difficult to capture when conducting long-term forecasting. This paper proposes a Legendre polynomial projection and information exchange architecture (LPPIEA) tailored for long-term time series forecasting. Reversible instance data normalization is introduced to reduce the influence of distribution shifts in long-term time series on predictions. Legendre polynomial projection is employed to handle complex temporal patterns, acquiring high-dimensional feature representations of the data to enhance the model inference capability for long-term time series. To effectively capture long-term temporal dependencies, a lightweight information exchange architecture is constructed to efficiently capture such dependencies, thus achieving accurate and efficient long-term time series forecasting. Experimental results on four commonly used public datasets demonstrate that the LPPIEA model reduces prediction errors by an average of 11.4% compared to baseline methods, while exhibiting higher computational efficiency.

Key words: time series forecasting, long-term temporal dependencies, polynomial projection, information exchange architecture, deep learning

刘建鑫, 马廷淮, 苏昱铭, 荣欢. 面向长期时间序列预测的多项式投影与信息交换架构[J]. 计算机工程与应用, 2025, 61(10): 120-132.

LIU Jianxin, MA Tinghuai, SU Yuming, RONG Huan. Polynomial Projection and Information Exchange Architecture for Long-Term Time Series Forecasting[J]. Computer Engineering and Applications, 2025, 61(10): 120-132.

参考文献

[1] CHENG Y, XING W, PEDRYCZ W, et al. NFIG-X: non-linear fuzzy information granule series for long-term traffic flow time series forecasting[J]. IEEE Transactions on Fuzzy Systems, 2023, 31(10): 3582-3597.
[2] AL-ALIMI D, ALRASSAS A M, AL-QANESS M A, et al. TLIA: time-series forecasting model using long short-term memory integrated with artificial neural networks for volatile energy markets[J]. Applied Energy, 2023, 343: 121230.
[3] ZHOU H Y, ZHANG S H, PENG J Q, et al. Informer: beyond efficient transformer for long sequence time-series forecasting[J]. Proceedings of the AAAI Conference on Artificial Intelligence, 2021, 35(12): 11106-11115.
[4] CAO H Z, HUANG Z H, YAO T C, et al. InParformer: evolutionary decomposition transformers with interactive parallel attention for long-term time series forecasting[J]. Proceedings of the AAAI Conference on Artificial Intelligence, 2023, 37(6): 6906-6915.
[5] OLIVARES K G, CHALLU C, MARCJASZ G, et al. Neural basis expansion analysis with exogenous variables: forecasting electricity prices with NBEATSx[J]. International Journal of Forecasting, 2023, 39(2): 884-900.
[6] ZHOU T, MA Z Q, WEN Q S, et al. FEDformer: frequency enhanced decomposed transformer for long-term series forecasting[C]//Proceedings of the 2022 International Conference on Machine Learning, 2022: 27268-27286.
[7] WU H X, XU J H, WANG J M, et al. Autoformer: decomposition transformers with auto-correlation for long-term series forecasting[C]//Advances in Neural Information Processing Systems 34, 2021: 22419-22430.
[8] WANG X Y, LIU H, DU J Z, et al. CLformer: locally grouped auto-correlation and convolutional transformer for long-term multivariate time series forecasting[J]. Engineering Applications of Artificial Intelligence, 2023, 121: 106042.
[9] WANG H S, ZHANG Y P, LIANG J, et al. DAFA-BiLSTM: deep autoregression feature augmented bidirectional LSTM network for time series prediction[J]. Neural Networks, 2023, 157: 240-256.
[10] LI Y T, WU K, LIU J. Self-paced ARIMA for robust time series prediction[J]. Knowledge-Based Systems, 2023, 269: 110489.
[11] ZHANG C, PENG T, NAZIR M S. A novel hybrid approach based on variational heteroscedastic Gaussian process regression for multi-step ahead wind speed forecasting[J]. International Journal of Electrical Power & Energy Systems, 2022, 136: 107717.
[12] VENKATACHALAM K, TROJOVSKY P, PAMUCAR D, et al. DWFH: an improved data-driven deep weather forecasting hybrid model using transductive long short term memory (T-LSTM)[J]. Expert Systems with Applications, 2023, 213: 119270.
[13] BACANIN N, JOVANOVIC L, ZIVKOVIC M, et al. Multivariate energy forecasting via metaheuristic tuned long-short term memory and gated recurrent unit neural networks[J]. Information Sciences, 2023, 642: 119122.
[14] 李文, 陈佳伟, 刘瑞雪, 等. 张量时间序列预测T-Transformer模型[J]. 计算机工程与应用, 2023, 59(11): 57-62.
LI W, CHEN J W, LIU R X, et al. T-Transformer model for predicting tensor time series[J]. Computer Engineering and Applications, 2023, 59(11): 57-62.
[15] LI S Y, JIN X Y, XUAN Y, et al. Enhancing the locality and breaking the memory bottleneck of transformer on time series forecasting[C]//Advances in Neural Information Processing Systems 32, 2019: 5243-5253.
[16] KITAEV N, KAISER ?, LEVSKAYA A. Reformer: the efficient transformer[C]//Proceedings of the 8th International Conference on Learning Representations, 2020.
[17] WANG H Q, PENG J, HUANG F H, et al. MICN: multi-scale local and global context modeling for long-term series forecasting[C]//Proceedings of the 11th International Conference on Learning Representations, 2023.
[18] SEN R, YU H F, DHILLON I. Think globally, act locally: a deep neural network approach to high-dimensional time series forecasting[C]//Advances in Neural Information Processing Systems 32, 2019: 4837-4846.
[19] LANGE H, BRUNTON S L, KUTZ J N. From Fourier to Koopman: spectral methods for long-term time series prediction[J]. Journal of Machine Learning Research, 2021, 22(1): 1881-1918.
[20] RADOJI?I? D, KREDATUS S. The impact of stock market price Fourier transform analysis on the gated recurrent unit classifier model[J]. Expert Systems with Applications, 2020, 159: 113565.
[21] GUPTA G, XIAO X Y, BOGDAN P, et al. Multiwavelet-based operator learning for differential equations[C]//Advances in Neural Information Processing Systems 34, 2021: 24048-24062.
[22] VOELKER A R, KAJI? I, ELIASMITH C. Legendre memory units: continuous-time representation in recurrent neural networks[C]//Advances in Neural Information Processing Systems 32, 2019: 15544-15553.
[23] GU A, DAO T, ERMON S, et al. Hippo: recurrent memory with optimal polynomial projections[C]//Advances in Neural Information Processing Systems 33, 2020: 1474-1487.
[24] KIM T, KIM J, TAE Y, et al. Reversible instance normalization for accurate time-series forecasting against distribution shift[C]//Proceedings of the 9th International Conference on Learning Representations, 2021.
[25] SA C D, GU A, PUTTAGUNTA R, et al. A two-pronged progress in structured dense matrix vector multiplication[C]//Proceedings of the 29th Annual ACM-SIAM Symposium on Discrete Algorithms. New York: ACM, 2018: 1060-1079.