基于多尺度时频域学习的多元长时间序列预测

doi:10.19665/j.issn1001-2400.20241207

摘要/Abstract

摘要：

针对现有多元长时间序列预测模型中存在的两个问题,一是仅利用单周期尺度时域信息无法捕捉序列的长期时间依赖关系,二是难以捕捉到有效的多元依赖关系。基于多层感知机,提出了一种基于多尺度时频域学习的多元长时间序列预测模型。模型首先基于傅里叶变换自适应寻找序列的不同周期作为多个尺度;然后针对每个尺度,通过序列分解,分别进行时域和频域两阶段的学习,获取序列的局部和全局时间依赖关系;随后再依据变量间的相关性分析结果,自适应建模多元序列的变量依赖关系;最后,对各尺度中不同的序列分解项应用不同的聚合方法,实现多尺度信息的互补融合。在七个真实数据集上的实验表明,该模型在超过90%的测试中位于最优或次优水平。与基于序列分解的线性模型DLinear相比,MSE实现了11%的平均降低和49.22%的最大降低,MAE实现了10%的平均降低和33.03%的最大降低。此外,模型在有效提升预测精度的同时,具有更高的运行效率。

关键词: 预测, 时间序列, 时频域, 多尺度, 序列分解, 多层感知机

Abstract:

To address two key issues in existing multivariate long-term series forecasting models—namely,the inability to capture long-term dependencies using single-period scale time-domain information,and the difficulty in capturing effective multivariate dependencies—a multivariate long-term series forecasting model based on multi-scale time-frequency domain learning is proposed by utilizing multilayer perceptrons.The model first employs the Fourier transform to adaptively identify different periods of the sequence as multiple scales.Then,for each scale,the sequence is decomposed to conduct two-stage learning in both the time and frequency domains,capturing local and global temporal dependencies.Subsequently,based on the results of correlation analysis among the variables,the model adaptively constructs the variable dependencies within the multivariate time series.Finally,different aggregation methods are applied to the decomposed components of the sequence across different scales to achieve complementary integration of multi-scale information.Experiments on seven real-world datasets demonstrate that this model achieves an optimal or suboptimal performance in over 90% of tests.Compared to the linear model DLinear based on sequence decomposition,the proposed model achieves an average reduction of 11% and a maximum reduction of 49.22% in MSE,as well as an average reduction of 10% and a maximum reduction of 33.03% in MAE.Furthermore,the model enhances the forecasting accuracy while also demonstrating an advanced operational efficiency.

Key words: forecasting, time series, time-frequency domain, multi-scale, sequence decomposition, multilayer perceptrons

中图分类号:

TP391

衡红军, 李怡欣. 基于多尺度时频域学习的多元长时间序列预测[J]. 西安电子科技大学学报, 2025, 52(2): 128-142.

HENG Hongjun, LI Yixin. Multivariate long-term series forecasting based on multi-scale time-frequency domain learning[J]. Journal of Xidian University, 2025, 52(2): 128-142.

图/表 14

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7个数据集上的多元长时间序列预测结果"

模型指标			MTFMixer			SparseTSF			NLinear			DLinear			Pathformer			PatchTST			TimesNet			Crossformer
模型指标			MSE	MAE		MSE	MAE		MSE	MAE		MSE	MAE		MSE	MAE		MSE	MAE		MSE	MAE		MSE	MAE
	96		0.293	0.343		0.303	0.347		0.300	0.349		0.333	0.387		0.301	0.347		0.302	0.348		0.340	0.374		0.745	0.584
	192		0.369	0.393		0.386	0.395		0.387	0.401		0.477	0.476		0.373	0.394		0.388	0.400		0.402	0.414		0.877	0.656
ETTh2	336		0.414	0.427		0.421	0.428		0.426	0.435		0.594	0.541		0.425	0.432		0.426	0.433		0.452	0.452		1.043	0.731
	720		0.422	0.440		0.422	0.437		0.432	0.451		0.831	0.657		0.433	0.448		0.431	0.446		0.462	0.468		1.104	0.763
	平均		0.375	0.401		0.383	0.402		0.386	0.409		0.559	0.515		0.383	0.405		0.387	0.407		0.414	0.427		0.942	0.684
	96		0.176	0.256		0.184	0.267		0.183	0.267		0.193	0.292		0.177	0.263		0.175	0.259		0.187	0.267		0.287	0.366
	192		0.241	0.302		0.248	0.304		0.247	0.305		0.284	0.362		0.241	0.304		0.241	0.302		0.249	0.309		0.414	0.492
ETTm2	336		0.298	0.339		0.308	0.343		0.308	0.344		0.369	0.427		0.300	0.340		0.305	0.343		0.321	0.351		0.597	0.542
	720		0.396	0.396		0.409	0.398		0.409	0.400		0.554	0.522		0.404	0.399		0.402	0.400		0.408	0.403		1.730	1.402
	平均		0.279	0.323		0.287	0.328		0.287	0.329		0.350	0.401		0.281	0.327		0.281	0.326		0.291	0.333		0.757	0.701
	96		0.376	0.397		0.401	0.406		0.402	0.410		0.386	0.400		0.393	0.401		0.414	0.419		0.384	0.402		0.423	0.448
	192		0.430	0.43 1		0.449	0.432		0.450	0.437		0.436	0.432		0.437	0.427		0.460	0.445		0.436	0.429		0.471	0.474
ETTh1	336		0.481	0.453		0.481	0.446		0.490	0.456		0.491	0.459		0.477	0.458		0.501	0.466		0.491	0.469		0.570	0.546
	720		0.498	0.496		0.460	0.454		0.486	0.475		0.521	0.516		0.489	0.479		0.500	0.488		0.521	0.500		0.653	0.621
	平均		0.447	0.444		0.448	0.435		0.457	0.445		0.459	0.452		0.449	0.441		0.469	0.455		0.458	0.450		0.529	0.522
	96		0.320	0.359		0.353	0.373		0.354	0.374		0.345	0.372		0.339	0.372		0.329	0.367		0.338	0.375		0.404	0.426
	192		0.363	0.382		0.393	0.392		0.391	0.392		0.380	0.389		0.380	0.390		0.367	0.385		0.374	0.387		0.450	0.451
ETTm1	336		0.398	0.406		0.424	0.412		0.424	0.414		0.413	0.413		0.406	0.410		0.399	0.410		0.410	0.411		0.532	0.515
	720		0.464	0.444		0.486	0.445		0.489	0.450		0.474	0.453		0.479	0.448		0.454	0.439		0.478	0.450		0.666	0.589
	平均		0.386	0.398		0.414	0.406		0.415	0.408		0.403	0.407		0.401	0.405		0.387	0.400		0.400	0.406		0.513	0.495
	96		0.083	0.200		0.094	0.218		0.084	0.201		0.093	0.224		0.093	0.216		0.088	0.205		0.107	0.234		0.256	0.367
	192		0.173	0.295		0.183	0.306		0.175	0.296		0.175	0.314		0.187	0.310		0.176	0.299		0.226	0.344		0.470	0.509
汇率	336		0.324	0.411		0.325	0.413		0.329	0.414		0.344	0.451		0.359	0.434		0.301	0.397		0.367	0.448		1.268	0.883
	720		0.833	0.686		0.856	0.700		0.886	0.711		0.901	0.714		0.976	0.748		0.901	0.714		0.964	0.746		1.767	1.068
	平均		0.353	0.398		0.365	0.409		0.369	0.406		0.378	0.426		0.404	0.427		0.367	0.404		0.416	0.443		0.940	0.707
	96		0.168	0.266		0.210	0.280		0.205	0.288		0.197	0.282		0.173	0.267		0.195	0.285		0.168	0.272		0.219	0.314
	192		0.181	0.272		0.205	0.281		0.205	0.289		0.196	0.285		0.184	0.273		0.199	0.289		0.184	0.289		0.231	0.322
电力	336		0.198	0.297		0.219	0.297		0.219	0.303		0.209	0.301		0.203	0.291		0.215	0.305		0.198	0.300		0.246	0.337
	720		0.242	0.333		0.260	0.328		0.262	0.336		0.245	0.333		0.238	0.320		0.256	0.337		0.220	0.320		0.280	0.363
	平均		0.197	0.292		0.224	0.297		0.223	0.304		0.212	0.300		0.200	0.288		0.216	0.304		0.193	0.295		0.244	0.334
	96		0.169	0.218		0.197	0.237		0.197	0.237		0.196	0.255		0.158	0.208		0.177	0.218		0.172	0.220		0.158	0.230
	192		0.217	0.256		0.243	0.273		0.243	0.274		0.237	0.296		0.209	0.256		0.225	0.259		0.219	0.261		0.206	0.277
天气	336		0.276	0.296		0.294	0.309		0.294	0.309		0.283	0.335		0.273	0.300		0.278	0.297		0.280	0.306		0.272	0.335
	720		0.351	0.347		0.366	0.355		0.368	0.357		0.345	0.381		0.351	0.347		0.354	0.348		0.365	0.359		0.398	0.418
	平均		0.254	0.279		0.275	0.294		0.276	0.294		0.265	0.317		0.248	0.278		0.259	0.281		0.259	0.287		0.259	0.315
最优个数		45			7			0			0			12			8			5			3

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数据集	数据维度	时间步数	采样频率	备注
ETTh1/h2	7	17 420	1小时	能源
ETTm1/m2	7	69 680	15分钟	能源
汇率	8	7 588	1天	金融
电力	321	26 304	1小时	能源
天气	21	52 696	10分钟	天气