综述35年时间序列长周期预测研究，解析误差累积机制与模型改进路径。
A Review of the Long Horizon Forecasting Problem in Time Series Analysis
- 梳理深度学习在趋势、季节性等分解方法上的融合创新
- 揭示长周期预测误差随时序增长的规律，xLSTM与Triformer表现更优
- 适合关注时间序列建模与工业预测的科研与工程人员阅读
长周期时间序列预测（LHF）问题在近35年中持续受到关注。本文回顾了该领域的发展历程，探讨深度学习如何结合趋势、季节性、傅里叶与小波变换、误设偏差降低及带通滤波等方法，并引入卷积、残差连接、稀疏性减少、步幅卷积、注意力掩码、状态空间模型（SSMs）、归一化、低秩近似与门控机制等技术。重点分析了时序分解、数据预处理与窗口划分对性能的提升作用。介绍了多层感知机、循环神经网络混合模型、自注意力模型在特征空间构建中的应用。基于ETTm2数据集，在多变量与单变量高有用载荷（HUFL）预测场景下，对最后4个月测试集进行消融实验。测试集各时间步平均均方误差热图显示，除xLSTM与Triformer外，误差随预测长度呈稳定上升趋势，表明长周期预测本质为误差传播问题。模型代码已公开：https://bit.ly/LHFModelZoo
原文摘要 · Abstract (English)
The long horizon forecasting (LHF) problem has come up in the time series literature for over the last 35 years or so. This review covers aspects of LHF in this period and how deep learning has incorporated variants of trend, seasonality, fourier and wavelet transforms, misspecification bias reduction and bandpass filters while contributing using convolutions, residual connections, sparsity reduction, strided convolutions, attention masks, SSMs, normalization methods, low-rank approximations and gating mechanisms. We highlight time series decomposition techniques, input data preprocessing and dataset windowing schemes that improve performance. Multi-layer perceptron models, recurrent neural network hybrids, self-attention models that improve and/or address the performances of the LHF problem are described, with an emphasis on the feature space construction. Ablation studies are conducted over the ETTm2 dataset in the multivariate and univariate high useful load (HUFL) forecasting contexts, evaluated over the last 4 months of the dataset. The heatmaps of MSE averages per time step over test set series in the horizon show that there is a steady increase in the error proportionate to its length except with xLSTM and Triformer models and motivate LHF as an error propagation problem. The trained models are available here: https://bit.ly/LHFModelZoo
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