Time series forecasting model based on dynamic weighted ensemble

doi:10.11772/j.issn.1001-9081.2025060707

Journal of Computer Applications ›› 2026, Vol. 46 ›› Issue (6): 1863-1871.DOI: 10.11772/j.issn.1001-9081.2025060707

• Data science and technology • Previous Articles

Time series forecasting model based on dynamic weighted ensemble

Xinru LIU¹, Songhua LIU²(), Lusha QI², Yaofei MENG²

^1.College of Computer Science and Technology （College of Data Science），Taiyuan University of Technology，Jinzhong Shanxi 030600，China
^2.School of Software，Taiyuan University of Technology，Jinzhong Shanxi 030600，China

Received:2025-06-24 Revised:2025-10-05 Accepted:2025-10-16 Online:2025-10-23 Published:2026-06-10
Contact: Songhua LIU
About author:LIU Xinru， born in 2000， M. S. candidate. Her research interests include time series forecasting， ensemble learning.
QI Lusha， born in 2001， M. S. candidate. Her research interests include data mining， time series forecasting.
MENG Yaofei， born in 2002. His research interests include data mining， time series forecasting.
First author contact:LIU Songhua， born in 1981， Ph. D.， associate professor. His research interests include data mining， time series.
Supported by:
National Natural Science Foundation of China(62476190);Natural Science Foundation of Shanxi Province(202203021211144)

基于动态加权集成的时序预测模型

刘新如¹, 刘松华²(), 祁露莎², 孟耀飞²

^1.太原理工大学计算机科学与技术学院（大数据学院），山西晋中 030600
^2.太原理工大学软件学院，山西晋中 030600

通讯作者: 刘松华
作者简介:刘新如（2000—），女，河南开封人，硕士研究生，CCF会员，主要研究方向：时序预测、集成学习
祁露莎（2001—），女，山西晋城人，硕士研究生，主要研究方向：数据挖掘、时序预测
孟耀飞（2002—），男，山西忻州人，主要研究方向：数据挖掘、时序预测。
第一联系人：刘松华（1981—），男，山西河曲人，副教授，博士，主要研究方向：数据挖掘、时间序列
基金资助:
国家自然科学基金资助项目(62476190);山西省自然科学基金资助项目(202203021211144)

Abstract

Abstract:

To address the inadequate adaptability under rapidly changing data distribution and the difficulty in balancing prediction accuracy with computational overhead of the existing time series forecasting methods， a time series forecasting model based on dynamic weighted ensemble， namely TFEM （Time-Frequency Ensembled Model）， was proposed. Firstly， in the time domain module， a Low-Rank Self-Attention （LRSA） mechanism was designed to calculate attention through projecting high-dimensional features into a low-dimensional space， which reduced complexity while maintaining long-range dependency modeling. Simultaneously， in the frequency domain module， the signal was decomposed into dominant frequency components and non-stationary residuals to model global trends and local mutations， respectively， thereby enhancing the modeling capability for complex time series. Finally， at the ensemble level， a long- and short-term harmonic balanced weighting mechanism was proposed， where long-term weights was used to capture global trends robustly through recursive update， while short-term weights was used to respond to data distribution mutations promptly via a Multi-Layer Perceptron （MLP）， and a smoothing factor was incorporated to suppress violent fluctuations in weights. Experimental results demonstrate that compared with the online ensemble model OneNet （Online Network）， TFEM reduces the Mean Squared Error （MSE） by 6.4% to 44.8% and the Mean Absolute Error （MAE） by 2.8% to 17.6% on seven benchmark datasets， while reduces the parameter number by 69.4% and inference time by 50.5% on the ETTh1 dataset. It can be seen that TFEM enhances prediction accuracy while reducing computational overhead， providing a feasible solution for time series forecasting in resource-constrained scenarios.

Key words: time series, ensemble learning, time domain, frequency domain, dynamic weighting

摘要：

针对现有时间序列预测方法在数据分布快速变化时适应性不足且难以平衡预测精度与时空开销的问题，提出一种基于动态加权集成的时序预测模型TFEM（Time-Frequency Ensembled Model）。首先，在时域模块中设计低秩自注意力（LRSA）机制，通过将高维特征投影至低维空间计算注意力，在降低复杂度的同时保持长程依赖建模；同时，在频域模块中将信号分解为主导频率分量和非平稳残差，分别建模全局趋势与局部突变，提升对复杂时序的建模能力；最后，在集成层面提出长短期谐衡加权机制，其中长期权重通过递归更新稳健捕捉全局趋势，短期权重借助多层感知机（MLP）及时响应数据分布的突变，并结合平滑因子抑制权重的剧烈波动。实验结果表明：与在线集成的模型OneNet （Online Network）相比，TFEM在7个基准数据集上的均方误差（MSE）降低了6.4%~44.8%，平均绝对误差（MAE）降低了2.8%~17.6%；且在ETTh1数据集上的参数量减少了69.4%，推理时间减少了50.5%。可见，TFEM在提升预测精度的同时能够降低计算开销，为资源受限场景下的时序预测提供了可行方案。

关键词: 时间序列, 集成学习, 时域, 频域, 动态加权

CLC Number:

TP391.1

Xinru LIU, Songhua LIU, Lusha QI, Yaofei MENG. Time series forecasting model based on dynamic weighted ensemble[J]. Journal of Computer Applications, 2026, 46(6): 1863-1871.

刘新如, 刘松华, 祁露莎, 孟耀飞. 基于动态加权集成的时序预测模型[J]. 《计算机应用》唯一官方网站, 2026, 46(6): 1863-1871.

Figures/Tables 14

Fig. 1 Architecture of TFEM model

Fig. 2 Structure of short-term weighting mechanism

Tab. 1 Basic information of datasets

数据集	属性数	时间步	粒度/min
ETTh1，ETTh2	7	17 420	60
ETTm1，ETTm1	7	69 680	15
Weather	21	52 696	10
Exchange_Rate	8	7 588	1 440
ILI	7	966	10 080

Tab. 2 Prediction errors of various models on benchmark datasets

数据集	预测长度	TFEM		DLinear		PatchTST		iTransformer		TimesNet		ATFNet		OneNet
数据集	预测长度	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.268	0.345	0.375	0.399	0.370	0.400	0.386	0.405	0.384	0.402	0.405	0.442	0.275	0.354
	192	0.284	0.355	0.405	0.416	0.413	0.429	0.441	0.436	0.436	0.429	0.467	0.482	0.287	0.359
	336	0.284	0.358	0.439	0.443	0.422	0.440	0.487	0.458	0.491	0.469	0.514	0.521	0.293	0.369
	720	0.280	0.356	0.472	0.490	0.447	0.468	0.503	0.491	0.521	0.500	0.614	0.589	0.310	0.371
ETTh2	96	0.122	0.238	0.289	0.353	0.274	0.337	0.297	0.349	0.340	0.374	0.171	0.282	0.096	0.218
	192	0.128	0.244	0.383	0.418	0.341	0.382	0.380	0.400	0.402	0.414	0.211	0.315	0.195	0.313
	336	0.136	0.253	0.448	0.465	0.329	0.384	0.428	0.432	0.452	0.452	0.236	0.344	0.186	0.301
	720	0.138	0.255	0.605	0.551	0.379	0.422	0.427	0.445	0.462	0.468	0.297	0.399	0.189	0.304
ETTm1	96	0.105	0.224	0.299	0.343	0.293	0.346	0.334	0.368	0.338	0.375	0.327	0.375	0.111	0.229
	192	0.112	0.232	0.335	0.365	0.333	0.370	0.377	0.391	0.374	0.487	0.370	0.412	0.118	0.237
	336	0.117	0.238	0.369	0.386	0.369	0.392	0.426	0.420	0.410	0.411	0.402	0.438	0.121	0.241
	720	0.131	0.251	0.425	0.421	0.416	0.420	0.491	0.459	0.478	0.450	0.453	0.476	0.147	0.265
ETTm2	96	0.057	0.157	0.167	0.260	0.166	0.256	0.180	0.264	0.187	0.267	0.114	0.227	0.064	0.162
	192	0.059	0.160	0.224	0.303	0.223	0.296	0.250	0.309	0.249	0.309	0.141	0.254	0.068	0.168
	336	0.062	0.163	0.280	0.334	0.274	0.329	0.311	0.348	0.321	0.351	0.172	0.281	0.076	0.180
	720	0.068	0.172	0.364	0.385	0.362	0.385	0.412	0.407	0.408	0.403	0.219	0.317	0.082	0.188
Weather	96	0.064	0.098	0.176	0.237	0.149	0.198	0.174	0.214	0.172	0.220	0.156	0.206	0.078	0.108
	192	0.064	0.100	0.220	0.282	0.194	0.241	0.221	0.254	0.219	0.261	0.199	0.246	0.086	0.115
	336	0.066	0.101	0.265	0.319	0.245	0.282	0.278	0.296	0.280	0.306	0.249	0.286	0.090	0.121
	720	0.070	0.104	0.323	0.362	0.314	0.334	0.358	0.347	0.365	0.359	0.311	0.335	0.103	0.128
Exchange_Rate	96	0.016	0.083	0.084	0.216	0.091	0.208	0.086	0.206	0.107	0.234	0.097	0.219	0.033	0.100
	192	0.019	0.090	0.157	0.298	0.175	0.298	0.177	0.299	0.226	0.344	0.239	0.342	0.039	0.106
	336	0.018	0.087	0.236	0.379	0.355	0.425	0.331	0.417	0.367	0.448	0.367	0.445	0.042	0.113
	720	0.042	0.105	0.626	0.634	0.974	0.733	0.847	0.691	0.964	0.746	0.645	0.611	0.058	0.124
ILI	24	0.928	0.666	3.015	1.192	1.319	0.754	1.500	0.823	2.317	0.934	1.543	0.798	1.481	0.783
	36	0.934	0.657	2.737	1.036	1.579	0.870	1.482	0.812	1.972	0.920	1.607	0.825	1.429	0.790
	48	0.967	0.672	2.577	1.043	1.553	0.815	1.607	0.862	2.238	0.940	1.650	0.844	1.424	0.813
	60	0.944	0.660	2.821	1.091	1.470	0.788	1.882	0.969	2.027	0.928	2.156	1.014	1.461	0.836

Tab. 2 Prediction errors of various models on benchmark datasets

数据集	预测长度	TFEM		DLinear		PatchTST		iTransformer		TimesNet		ATFNet		OneNet
数据集	预测长度	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.268	0.345	0.375	0.399	0.370	0.400	0.386	0.405	0.384	0.402	0.405	0.442	0.275	0.354
	192	0.284	0.355	0.405	0.416	0.413	0.429	0.441	0.436	0.436	0.429	0.467	0.482	0.287	0.359
	336	0.284	0.358	0.439	0.443	0.422	0.440	0.487	0.458	0.491	0.469	0.514	0.521	0.293	0.369
	720	0.280	0.356	0.472	0.490	0.447	0.468	0.503	0.491	0.521	0.500	0.614	0.589	0.310	0.371
ETTh2	96	0.122	0.238	0.289	0.353	0.274	0.337	0.297	0.349	0.340	0.374	0.171	0.282	0.096	0.218
	192	0.128	0.244	0.383	0.418	0.341	0.382	0.380	0.400	0.402	0.414	0.211	0.315	0.195	0.313
	336	0.136	0.253	0.448	0.465	0.329	0.384	0.428	0.432	0.452	0.452	0.236	0.344	0.186	0.301
	720	0.138	0.255	0.605	0.551	0.379	0.422	0.427	0.445	0.462	0.468	0.297	0.399	0.189	0.304
ETTm1	96	0.105	0.224	0.299	0.343	0.293	0.346	0.334	0.368	0.338	0.375	0.327	0.375	0.111	0.229
	192	0.112	0.232	0.335	0.365	0.333	0.370	0.377	0.391	0.374	0.487	0.370	0.412	0.118	0.237
	336	0.117	0.238	0.369	0.386	0.369	0.392	0.426	0.420	0.410	0.411	0.402	0.438	0.121	0.241
	720	0.131	0.251	0.425	0.421	0.416	0.420	0.491	0.459	0.478	0.450	0.453	0.476	0.147	0.265
ETTm2	96	0.057	0.157	0.167	0.260	0.166	0.256	0.180	0.264	0.187	0.267	0.114	0.227	0.064	0.162
	192	0.059	0.160	0.224	0.303	0.223	0.296	0.250	0.309	0.249	0.309	0.141	0.254	0.068	0.168
	336	0.062	0.163	0.280	0.334	0.274	0.329	0.311	0.348	0.321	0.351	0.172	0.281	0.076	0.180
	720	0.068	0.172	0.364	0.385	0.362	0.385	0.412	0.407	0.408	0.403	0.219	0.317	0.082	0.188
Weather	96	0.064	0.098	0.176	0.237	0.149	0.198	0.174	0.214	0.172	0.220	0.156	0.206	0.078	0.108
	192	0.064	0.100	0.220	0.282	0.194	0.241	0.221	0.254	0.219	0.261	0.199	0.246	0.086	0.115
	336	0.066	0.101	0.265	0.319	0.245	0.282	0.278	0.296	0.280	0.306	0.249	0.286	0.090	0.121
	720	0.070	0.104	0.323	0.362	0.314	0.334	0.358	0.347	0.365	0.359	0.311	0.335	0.103	0.128
Exchange_Rate	96	0.016	0.083	0.084	0.216	0.091	0.208	0.086	0.206	0.107	0.234	0.097	0.219	0.033	0.100
	192	0.019	0.090	0.157	0.298	0.175	0.298	0.177	0.299	0.226	0.344	0.239	0.342	0.039	0.106
	336	0.018	0.087	0.236	0.379	0.355	0.425	0.331	0.417	0.367	0.448	0.367	0.445	0.042	0.113
	720	0.042	0.105	0.626	0.634	0.974	0.733	0.847	0.691	0.964	0.746	0.645	0.611	0.058	0.124
ILI	24	0.928	0.666	3.015	1.192	1.319	0.754	1.500	0.823	2.317	0.934	1.543	0.798	1.481	0.783
	36	0.934	0.657	2.737	1.036	1.579	0.870	1.482	0.812	1.972	0.920	1.607	0.825	1.429	0.790
	48	0.967	0.672	2.577	1.043	1.553	0.815	1.607	0.862	2.238	0.940	1.650	0.844	1.424	0.813
	60	0.944	0.660	2.821	1.091	1.470	0.788	1.882	0.969	2.027	0.928	2.156	1.014	1.461	0.836

Fig.3 MSEs of TFEM and some representative models under different prediction lengths

Fig. 4 Prediction performance of TFEM on various datasets

Tab. 3 ADF test results

数据集

概率值

ADF

统计量

临界值

（1%）

临界值

（5%）

临界值

（10%）

Fig. 5 KL divergence changes on Exchange_Rate and ILI datasets

Tab. 4 Efficiency comparison between low-rank and standard self-attention mechanisms

机制	计算量/10⁹	参数量/10³	时间/ms	内存/MB
LRSA	0.40	131.8	0.81	24
MHSA	3.22	1 050.6	1.18	28

Tab. 5 Time complexity of different models

模型	时间复杂度	模型	时间复杂度
TFEM	$O (L 2 r)$	ATFNet	$O (L 2 d k)$
PatchTST	$O ((L / S) 2 M d k)$	OneNet	$O (L M 2 d k)$
DLinear	$O (L d k)$

Tab. 5 Time complexity of different models

模型	时间复杂度	模型	时间复杂度
TFEM	$O (L 2 r)$	ATFNet	$O (L 2 d k)$
PatchTST	$O ((L / S) 2 M d k)$	OneNet	$O (L M 2 d k)$
DLinear	$O (L d k)$

Tab. 6 Spatial-temporal overhead and prediction performance of different models

模型	参数量/10⁶	时间/s	内存/GB	MSE
TFEM	28.20	3.900 00	0.48	0.23
PatchTST	40.99	3.060 00	0.40	0.49
DLinear	0.53	0.000 34	0.02	0.68
ATFNet	143.30	10.620 00	1.20	0.51
OneNet	92.27	7.880 00	0.93	0.31

Tab. 7 Ablation experiment results on ensemble strategies

数据集	预测长度	TFEM		-W		-b		-EMA
数据集	预测长度	MSE	MAE	MSE	MAE	MSE	MAE	MSE	MAE
ETTh1	96	0.268	0.345	0.285	0.352	0.336	0.377	0.279	0.350
	192	0.284	0.355	0.307	0.367	0.359	0.391	0.285	0.356
	336	0.284	0.358	0.326	0.374	0.368	0.396	0.284	0.358
	720	0.280	0.356	0.310	0.372	0.382	0.412	0.287	0.363
ETTh2	96	0.122	0.238	0.141	0.251	0.186	0.286	0.122	0.238
	192	0.128	0.244	0.155	0.264	0.193	0.293	0.131	0.247
	336	0.136	0.253	0.158	0.268	0.406	0.430	0.139	0.254
	720	0.138	0.255	0.162	0.272	0.280	0.362	0.356	0.399
Weather	96	0.064	0.098	0.079	0.161	0.225	0.203	0.067	0.102
	192	0.064	0.100	0.085	0.173	0.231	0.232	0.065	0.105
	336	0.066	0.101	0.093	0.162	0.221	0.243	0.069	0.108
	720	0.070	0.104	0.102	0.151	0.211	0.263	0.074	0.110

Tab. 8 Spatio-temporal overhead and performance under different r

r	参数量/10⁶	推理时间/s	内存/GB	MSE
8	27.12	3.65	0.463	0.253
16	27.93	3.79	0.476	0.236
32	28.20	3.90	0.480	0.230
64	29.47	4.17	0.494	0.227

Fig.6 Impact of hyperparameters α and v on model performance

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Time series forecasting model based on dynamic weighted ensemble

基于动态加权集成的时序预测模型

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