Time series prediction model based on statistical distribution sensing and frequency domain dual-channel fusion

doi:10.11772/j.issn.1001-9081.2024121750

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (1): 113-123.DOI: 10.11772/j.issn.1001-9081.2024121750

• Data science and technology • Previous Articles Next Articles

Time series prediction model based on statistical distribution sensing and frequency domain dual-channel fusion

Junheng WU¹^,², Xiaodong WANG¹^,², Qixue HE¹^,²()

^1.Chengdu Institute of Computer Application，Chinese Academy of Sciences，Chengdu Sichuan 610213，China
^2.School of Computer Science and Technology，University of Chinese Academy of Sciences，Beijing 100049，China

Received:2024-12-12 Revised:2025-03-17 Accepted:2025-03-18 Online:2026-01-10 Published:2026-01-10
Contact: Qixue HE
About author:WU Junheng， born in 1998， M. S. candidate. His research interests include time series prediction， machine learning.
WANG Xiaodong， born in 1973， M. S.， senior engineer. His research interests include industrial modeling， internet of things， machine learning.
Supported by:
Key Research and Development Project in Sichuan Province(2024ZHCG0170)

基于统计分布感知与频域双通道融合的时序预测模型

吴俊衡¹^,², 王晓东¹^,², 何启学¹^,²()

^1.中国科学院成都计算机应用研究所，成都 610213
^2.中国科学院大学计算机科学与技术学院，北京 100049

通讯作者: 何启学
作者简介:吴俊衡（1998—），男，重庆人，硕士研究生，主要研究方向：时间序列预测、机器学习
王晓东（1973—），男，四川乐山人，高级工程师，硕士，主要研究方向：工业建模、物联网、机器学习
基金资助:
四川省重点研发项目(2024ZHCG0170)

Abstract

Abstract:

Aiming at the prediction difficulties caused by periodic complexity and high-frequency noise in time series data， a time series prediction model based on statistical distribution sensing and frequency domain dual-channel fusion was proposed to mitigate data drift， suppress noise interference， and improve prediction accuracy. Firstly， the original time series data was processed through window overlapping slices， the statistical distribution of data in each slice was calculated and normalized， and a MultiLayer Perceptron （MLP） was used to predict the statistical distribution of future data. Then， adaptive time-frequency transformation was performed to the normalized series， and the correlation features within the frequency domain and between channels were strengthened through the channel independent encoder and the channel interactive learner， so as to obtain multi-scale frequency domain representation. Finally， a linear prediction layer was used to complete the inverse transformation from the frequency domain to the time domain. In the output stage， the model used the statistical distribution of future data to perform inverse normalization，thereby generating the final prediction results. Comparison experimental results of the proposed model with the current mainstream time series prediction model PatchTST （Patch Time Series Transformer） show that on the Exchange， ETTm2， and Solar datasets， the model has the Mean Square Error （MSE） reduced by average of 5.3%， and the Mean Absolute Error （MAE） reduced by average of 4.0%， demonstrating good noise suppression capabilities and prediction performance. Ablation experimental results show that the all of data statistical distribution sensing， adaptive frequency domain processing， and dual-channel fusion modules have significant contributions for improving prediction accuracy.

Key words: time series prediction, time-frequency analysis, Transformer, channel independence, channel mixing

摘要：

针对时间序列数据中周期复杂性和高频噪声导致的预测困难，提出一种基于统计分布感知与频域双通道融合的时序预测模型，旨在缓解数据漂移、抑制噪声干扰并提高预测精度。首先，通过窗口重叠切片对原始时序数据进行处理，计算各切片的数据统计分布并进行归一化，再利用多层感知器（MLP）预测未来数据的统计分布；其次，将归一化后的序列经过自适应时频转换，并通过通道独立编码器和通道交互学习器强化频域内和通道间的关联特征，从而获取多尺度频域表征；最后，采用线性预测层完成频域到时域的逆变换，模型在输出阶段利用未来数据的统计分布进行逆归一化操作，从而生成最终预测结果。与当前主流的时序预测模型PatchTST （Patch Time Series Transformer）的对比实验结果表明，所提模型在Exchange、ETTm2和Solar数据集上的均方误差（MSE）平均降低了5.3%，平均绝对误差（MAE）平均降低了4.0%，体现了良好的噪声抑制能力和预测性能。消融实验结果进一步表明，数据统计分布感知、自适应频域与双通道融合模块在提升预测准确性方面都具有显著贡献。

关键词: 时间序列预测, 时频分析, Transformer, 通道独立, 通道混合

CLC Number:

TP399

Junheng WU, Xiaodong WANG, Qixue HE. Time series prediction model based on statistical distribution sensing and frequency domain dual-channel fusion[J]. Journal of Computer Applications, 2026, 46(1): 113-123.

吴俊衡, 王晓东, 何启学. 基于统计分布感知与频域双通道融合的时序预测模型[J]. 《计算机应用》唯一官方网站, 2026, 46(1): 113-123.

Figures/Tables 12

Fig. 1 Data drift phenomena

Fig. 2 Overall architecture of presented model

Fig. 3 Comparison of different acquisition modes for the same frequency component in Electricity dataset

Tab. 1 Time complexity and space complexity of different models

模型	时间复杂度	空间复杂度
本文模型	$O (L)$	$O (L)$
iTransformer^［28］	$O (L 2)$	$O (L 2)$
PatchTST^［18］	$O (L 2)$	$O (L 2)$
Crossformer^［16］	$O (L 2)$	$O (L 2)$
Autoformer^［14］	$O (L ⋅ l b (L))$	$O (L ⋅ l b (L))$
Informer^［13］	$O (L ⋅ l b (L))$	$O (L ⋅ l b (L))$
DLinear^［17］	$O (L)$	$O (L)$
Pyraformer^［15］	$O (L)$	$O (L)$

Tab. 1 Time complexity and space complexity of different models

模型	时间复杂度	空间复杂度
本文模型	$O (L)$	$O (L)$
iTransformer^［28］	$O (L 2)$	$O (L 2)$
PatchTST^［18］	$O (L 2)$	$O (L 2)$
Crossformer^［16］	$O (L 2)$	$O (L 2)$
Autoformer^［14］	$O (L ⋅ l b (L))$	$O (L ⋅ l b (L))$
Informer^［13］	$O (L ⋅ l b (L))$	$O (L ⋅ l b (L))$
DLinear^［17］	$O (L)$	$O (L)$
Pyraformer^［15］	$O (L)$	$O (L)$

Tab. 2 Basic information of datasets

数据集	采集时间间隔/min	维度	时间步数	平稳度系数
Exchange	1 440	8	7 588	-1.90
ETTm2	15	7	69 680	-5.66
Solar	10	137	52 560	-7.69
Electricity	60	321	26 304	-8.44
Weather	10	21	52 696	-26.68

Tab. 3 Comparison of prediction effects of different models on different datasets

数据集	预测长度	本文模型		PatchTST		iTransformer		DLinear		Crossformer		Autoformer		Informer
数据集	预测长度	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
Weather	96	0.145	0.197	0.151	0.200	0.163	0.212	0.176	0.237	0.226	0.301	0.301	0.343	0.354	0.405
	192	0.190	0.239	0.195	0.241	0.203	0.249	0.220	0.282	0.215	0.289	0.325	0.370	0.419	0.434
	336	0.243	0.283	0.247	0.281	0.255	0.289	0.265	0.319	0.319	0.317	0.351	0.391	0.583	0.543
	720	0.308	0.328	0.320	0.335	0.326	0.337	0.326	0.366	0.381	0.379	0.422	0.433	0.916	0.705
Exchange	96	0.079	0.199	0.093	0.215	0.088	0.209	0.122	0.264	0.135	0.278	0.182	0.312	0.836	0.773
	192	0.166	0.275	0.189	0.310	0.176	0.300	0.205	0.347	0.263	0.309	0.316	0.414	0.927	0.816
	336	0.312	0.401	0.343	0.425	0.323	0.414	0.332	0.440	0.442	0.519	0.519	0.535	1.078	0.874
	720	0.748	0.650	0.869	0.704	0.870	0.707	0.869	0.705	1.089	0.824	1.209	0.854	1.153	0.892
ETTm2	96	0.163	0.254	0.166	0.256	0.179	0.272	0.165	0.256	0.239	0.298	0.280	0.366	0.355	0.462
	192	0.222	0.295	0.223	0.296	0.241	0.315	0.226	0.306	0.307	0.346	0.310	0.371	0.595	0.586
	336	0.269	0.312	0.273	0.329	0.290	0.344	0.274	0.335	0.323	0.377	0.343	0.388	1.270	0.871
	720	0.355	0.379	0.361	0.385	0.376	0.397	0.380	0.408	0.405	0.429	0.412	0.433	3.999	1.704
Electricity	96	0.132	0.224	0.129	0.222	0.131	0.228	0.140	0.237	0.166	0.293	0.196	0.313	0.304	0.393
	192	0.149	0.241	0.148	0.240	0.155	0.249	0.153	0.249	0.187	0.302	0.211	0.324	0.327	0.417
	336	0.160	0.251	0.166	0.259	0.170	0.266	0.169	0.267	0.205	0.324	0.214	0.327	0.333	0.422
	720	0.192	0.283	0.210	0.298	0.207	0.300	0.203	0.301	0.211	0.338	0.236	0.342	0.351	0.427
Solar	96	0.174	0.214	0.194	0.249	0.201	0.260	0.221	0.289	0.241	0.299	0.266	0.311	0.208	0.237
	192	0.192	0.239	0.228	0.261	0.219	0.266	0.249	0.285	0.268	0.314	0.271	0.315	0.229	0.259
	336	0.210	0.248	0.221	0.254	0.218	0.266	0.263	0.291	0.288	0.311	0.281	0.317	0.235	0.272
	720	0.213	0.250	0.219	0.271	0.230	0.279	0.244	0.296	0.271	0.315	0.295	0.319	0.233	0.275
提升率/%				5.3	4.0	7.0	6.3	11.2	11.2	24.7	19.6	33.1	26.2	53.2	42.5

Fig. 4 Comparison of performance on the second dimension （perceived temperature）of Weather dataset with input length of 336 and output length of 96

Fig. 5 Comparison of performance on the 8th dimension （transformer oil temperature） of ETTm2 dataset with input length of 336 and output length of 720

Fig. 6 Comparison of performance on the third dimension （barometric pressure） of Solar dataset with input length of 336 and output length of 720

Fig. 7 Results of ablation experiments

Fig. 8 Impact of lookback window size on model performance

Fig. 9 Impact of slice length on model performance

References 37

[1]	杨汪洋，魏云冰，罗程浩. 基于CVMD-TCN-BiLSTM的短期电力负荷预测［J］. 电气工程学报，2024， 19（2）： 163-172.
	YANG W Y， WEI Y B， LUO C H. Short-term electricity load forecasting based on CVMD-TCN-BiLSTM［J］. Journal of Electrical Engineering， 2024， 19（2）： 163-172.
[2]	KAUSHIK S， CHOUDHURY A， SHERON P K， et al. AI in healthcare： time-series forecasting using statistical， neural， and ensemble architectures［J］. Frontiers in Big Data， 2020， 3： No.4.
[3]	HOU M， XU C， LI Z， et al. Multi-granularity residual learning with confidence estimation for time series prediction ［C］// Proceedings of the ACM Web Conference 2022. New York： ACM， 2022： 112-121.
[4]	王艺霏，于雷，滕飞，等. 基于长-短时序特征融合的资源负载预测模型［J］. 计算机应用，2022， 42（5）： 1508-1515.
	WANG Y F， YU L， TENG F， et al. Resource load prediction model based on long-short time series feature fusion［J］. Journal of Computer Applications， 2022， 42（5）： 1508-1515.
[5]	LIU Z， ZHU Z， GAO J， et al. Forecast methods for time series data： a survey［J］. IEEE Access， 2021， 9： 91896-91912.
[6]	WU H， HU T， LIU Y， et al. TimesNet： temporal 2D-variation modeling for general time series analysis［EB/OL］. ［2024-11-18］..
[7]	DENG A， HOOI B. Graph neural network-based anomaly detection in multivariate time series ［C］// Proceedings of the 35th AAAI Conference on Artificial Intelligence. Palo Alto： AAAI Press， 2021： 4027-4035.
[8]	VASWANI A， SHAZEER N， PARMAR N， et al. Attention is all you need ［C］// Proceedings of the 31st International Conference on Neural Information Processing Systems. Red Hook： Curran Associates Inc.， 2017： 6000-6010.
[9]	KALYAN K S， RAJASEKHARAN A， SANGEETHA S. AMMUS： a survey of transformer-based pretrained models in natural language processing［EB/OL］. ［2024-12-08］..
[10]	HAN K， WANG Y， CHEN H， et al. A survey on Vision Transformer［J］. IEEE Transactions on Pattern Analysis and Machine Intelligence， 2023， 45（1）： 87-110.
[11]	WEN Q， ZHOU T， ZHANG C， et al. Transformers in time series： a survey ［C］// Proceedings of the 32nd International Joint Conference on Artificial Intelligence. California： ijcai.org， 2023： 6778-6786.
[12]	ZHOU T， MA Z， WEN Q， et al. FEDformer： frequency enhanced decomposed transformer for long-term series forecasting ［C］// Proceedings of the 39th International Conference on Machine Learning. New York： JMLR.org， 2022： 27268-27286.
[13]	ZHOU H， ZHANG S， PENG J， et al. Informer： beyond efficient transformer for long sequence time-series forecasting ［C］// Proceedings of the 35th AAAI Conference on Artificial Intelligence. Palo Alto： AAAI Press， 2021： 11106-11115.
[14]	WU H， XU J， WANG J， et al. Autoformer： decomposition transformers with auto-correlation for long-term series forecasting ［C］// Proceedings of the 35th International Conference on Neural Information Processing Systems. Red Hook： Curran Associates Inc.， 2021： 22419-22430.
[15]	LIU S， YU H， LIAO C， et al. Pyraformer： low-complexity pyramidal attention for long-range time series modeling and forecasting［EB/OL］. ［2024-11-18］..
[16]	ZHANG Y， YAN J. Crossformer： Transformer utilizing cross-dimension dependency for multivariate time series forecasting［EB/OL］. ［2024-11-18］..
[17]	ZENG A， CHEN M， ZHANG L， et al. Are Transformers effective for time series forecasting？［C］// Proceedings of the 37th AAAI Conference on Artificial Intelligence. Palo Alto： AAAI Press， 2023： 11121-11128.
[18]	NIE Y， NGUYEN N H， SINTHONG P， et al. A time series is worth 64 words： long-term forecasting with Transformers［EB/OL］. ［2024-07-25］..
[19]	ZHANG X， JIN X， GOPALSWAMY K， et al. First de-trend then attend： rethinking attention for time-series forecasting［EB/OL］. ［2024-07-31］..
[20]	ZHANG X， ZHAO S， SONG Z， et al. Not all frequencies are created equal： towards a dynamic fusion of frequencies in time-series forecasting ［C］// Proceedings of the 32nd ACM International Conference on Multimedia. New York： ACM， 2024： 4729-4737.
[21]	PIAO X， CHEN Z， MURAYAMA T， et al. Fredformer： frequency debiased transformer for time series forecasting ［C］// Proceedings of the 30th ACM SIGKDD Conference on Knowledge Discovery and Data Mining. New York： ACM， 2024： 2400-2410.
[22]	JIANG M， ZENG P， WANG K， et al. FECAM： frequency enhanced channel attention mechanism for time series forecasting［J］. Advanced Engineering Informatics， 2023， 58： No.102158.
[23]	DU Y， WANG J， FENG W， et al. AdaRNN： adaptive learning and forecasting of time series ［C］// Proceedings of the 30th ACM International Conference on Information and Knowledge Management. New York： ACM， 2021： 402-411.
[24]	LIU Y， WU H， WANG J， et al. Non-stationary transformers： exploring the stationarity in time series forecasting ［C］// Proceedings of the 36th International Conference on Neural Information Processing Systems. Red Hook： Curran Associates Inc.， 2022： 9881-9893.
[25]	KIM T， KIM J， TAE Y， et al. Reversible instance normalization for accurate time-series forecasting against distribution shift［EB/OL］. ［2024-11-18］..
[26]	FAN W， WANG P， WANG D， et al. Dish-TS： a general paradigm for alleviating distribution shift in time series forecasting ［C］// Proceedings of the 37th AAAI Conference on Artificial Intelligence. Palo Alto： AAAI Press， 2023： 7522-7529.
[27]	QIU X， CHENG H， WU X， et al. A comprehensive survey of deep learning for multivariate time series forecasting： a channel strategy perspective［EB/OL］. ［2025-03-28］..
[28]	LIU Y， HU T， ZHANG H， et al. iTransformer： inverted Transformers are effective for time series forecasting［EB/OL］. ［2024-11-05］..
[29]	YI K， ZHANG Q， FAN W， et al. Frequency-domain MLPs are more effective learners in time series forecasting ［C］// Proceedings of the 37th International Conference on Neural Information Processing Systems. Red Hook： Curran Associates Inc.， 2024： 76656-76679.
[30]	QIU X， WU X， LIN Y， et al. DUET： dual clustering enhanced multivariate time series forecasting ［C］// Proceedings of the 31st ACM SIGKDD Conference on Knowledge Discovery and Data Mining V.1. New York： ACM， 2025： 1185-1196.
[31]	ZHOU L， WANG H. MST-GAT： a multi-perspective spatial-temporal graph attention network for multi-sensor equipment remaining useful life prediction［J］. Information Fusion， 2024， 110： No.102462.
[32]	LIU Z， CHENG M， LI Z， et al. Adaptive normalization for non-stationary time series forecasting： a temporal slice perspective ［C］// Proceedings of the 37th International Conference on Neural Information Processing Systems. Stroudsburg： ACL， 2023：14273-14292.
[33]	HE K， ZHANG X， REN S， et al. Deep residual learning for image recognition ［C］// Proceedings of the 2016 IEEE Conference on Computer Vision and Pattern Recognition. Piscataway： IEEE， 2016： 770-778.
[34]	WANG S， WU H， SHI X， et al. TimeMixer： decomposable multiscale mixing for time series forecasting［EB/OL］. ［2024-11-18］..
[35]	CHEN Y， LIU S， YANG J， et al. A Joint Time-Frequency Domain Transformer for multivariate time series forecasting［J］. Neural Networks， 2024， 176： No.106334.
[36]	LI Z， RAO Z， PAN L， et al. MTS-Mixers： multivariate time series forecasting via factorized temporal and channel mixing［EB/OL］. ［2024-10-24］..
[37]	MUSHTAQ R. Augmented dickey fuller test［EB/OL］. ［2024-12-25］..

Time series prediction model based on statistical distribution sensing and frequency domain dual-channel fusion

基于统计分布感知与频域双通道融合的时序预测模型

RichHTML

PDF

Knowledge

Abstract

Cite this article

share this article

Figures/Tables 12

References 37

Related Articles 15

Recommended Articles

Metrics

[1]	Lifang WANG, Wenjing REN, Xiaodong GUO, Rongguo ZHANG, Lihua HU. Trident generative adversarial network for low-dose CT image denoising [J]. Journal of Computer Applications, 2026, 46(1): 270-279.
[2]	Lijin YAO, Di ZHANG, Piyu ZHOU, Zhijian QU, Haipeng WANG. Transformer and gated recurrent unit-based de novo sequencing algorithm for phosphopeptides [J]. Journal of Computer Applications, 2026, 46(1): 297-304.
[3]	Yu SANG, Tong GONG, Chen ZHAO, Bowen YU, Siman LI. Domain-adaptive nighttime object detection method with photometric alignment [J]. Journal of Computer Applications, 2026, 46(1): 242-251.
[4]	Jinggang LYU, Shaorui PENG, Shuo GAO, Jin ZHOU. Speech enhancement network driven by complex frequency attention and multi-scale frequency enhancement [J]. Journal of Computer Applications, 2025, 45(9): 2957-2965.
[5]	Yiming LIANG, Jing FAN, Wenze CHAI. Multi-scale feature fusion sentiment classification based on bidirectional cross attention [J]. Journal of Computer Applications, 2025, 45(9): 2773-2782.
[6]	Jin LI, Liqun LIU. SAR and visible image fusion based on residual Swin Transformer [J]. Journal of Computer Applications, 2025, 45(9): 2949-2956.
[7]	Xiang WANG, Zhixiang CHEN, Guojun MAO. Multivariate time series prediction method combining local and global correlation [J]. Journal of Computer Applications, 2025, 45(9): 2806-2816.
[8]	Fang WANG, Jing HU, Rui ZHANG, Wenting FAN. Medical image segmentation network with content-guided multi-angle feature fusion [J]. Journal of Computer Applications, 2025, 45(9): 3017-3025.
[9]	Li LI, Han SONG, Peihe LIU, Hanlin CHEN. Named entity recognition for sensitive information based on data augmentation and residual networks [J]. Journal of Computer Applications, 2025, 45(9): 2790-2797.
[10]	Jing WANG, Jiaxing LIU, Wanying SONG, Jiaxing XUE, Wenxin DING. Few-shot skin image classification model based on spatial transformer network and feature distribution calibration [J]. Journal of Computer Applications, 2025, 45(8): 2720-2726.
[11]	Jin ZHOU, Yuzhi LI, Xu ZHANG, Shuo GAO, Li ZHANG, Jiachuan SHENG. Modulation recognition network for complex electromagnetic environments [J]. Journal of Computer Applications, 2025, 45(8): 2672-2682.
[12]	Yongpeng TAO, Shiqi BAI, Zhengwen ZHOU. Neural architecture search for multi-tissue segmentation using convolutional and transformer-based networks in glioma segmentation [J]. Journal of Computer Applications, 2025, 45(7): 2378-2386.
[13]	Haoyu LIU, Pengwei KONG, Yaoli WANG, Qing CHANG. Pedestrian detection algorithm based on multi-view information [J]. Journal of Computer Applications, 2025, 45(7): 2325-2332.
[14]	Dehui ZHOU, Jun ZHAO, Jinfeng CHENG. Tiny defect detection algorithm for bearing surface based on RT-DETR [J]. Journal of Computer Applications, 2025, 45(6): 1987-1997.
[15]	Sheping ZHAI, Yan HUANG, Qing YANG, Rui YANG. Multi-view entity alignment combining triples and text attributes [J]. Journal of Computer Applications, 2025, 45(6): 1793-1800.