Title: A Review of the Long Horizon Forecasting Problem in Time Series Analysis Show Chinese title

Title: 时间序列分析中长期预测问题的研究综述

Abstract: 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 Show Chinese abstract

Abstract: 长期预测（LHF）问题在时间序列文献中已经出现大约35年了。 本文综述了这一时期LHF的各个方面以及深度学习如何结合趋势、季节性、傅里叶和小波变换的变体、误设偏差减少和带通滤波器的改进方法，同时通过卷积、残差连接、稀疏性降低、步幅卷积、注意力掩码、状态空间模型（SSM）、归一化方法、低秩近似和门控机制作出贡献。 我们强调了有助于提高性能的时间序列分解技术、输入数据预处理和数据集窗口方案。 描述了多层感知器模型、循环神经网络混合模型和自注意力模型，这些模型改进了和/或解决了LHF问题的表现，并重点介绍了特征空间构造。 在多变量和单变量高负荷（HUFL）预测背景下，在ETTm2数据集上进行了消融研究，评估了数据集最后4个月的表现。 测试集序列在时间步长上的MSE平均热图显示，误差随着长度的增加而稳步上升，但xLSTM和Triformer模型除外，这表明LHF可以看作是一个误差传播问题。 训练好的模型在这里：https://bit.ly/LHFModelZoo