Forecasting models are pivotal in a data-driven world with vast volumes of time series data that appear as a compound of vast Linear and Nonlinear patterns. Recent deep time series forecasting models struggle to utilize seasonal and trend decomposition to separate the entangled components. Such a strategy only explicitly extracts simple linear patterns like trends, leaving the other linear modes and vast unexplored nonlinear patterns to the residual. Their flawed linear and nonlinear feature extraction models and shallow-level decomposition limit their adaptation to the diverse patterns present in real-world scenarios. Given this, we innovate Recursive Residual Decomposition by introducing explicit extraction of both linear and nonlinear patterns. This deeper-level decomposition framework, which is named LiNo, captures linear patterns using a Li block which can be a moving average kernel, and models nonlinear patterns using a No block which can be a Transformer encoder. The extraction of these two patterns is performed alternatively and recursively. To achieve the full potential of LiNo, we develop the current simple linear pattern extractor to a general learnable autoregressive model, and design a novel No block that can handle all essential nonlinear patterns. Remarkably, the proposed LiNo achieves state-of-the-art on thirteen real-world benchmarks under univariate and multivariate forecasting scenarios. Experiments show that current forecasting models can deliver more robust and precise results through this advanced Recursive Residual Decomposition. We hope this work could offer insight into designing more effective forecasting models. Code is available at this Repository: https://github.com/Levi-Ackman/LiNo.

翻译：在数据驱动的世界中，时间序列数据通常表现为大量线性与非线性模式的复合体，预测模型在其中起着关键作用。近期深度时间序列预测模型难以利用季节与趋势分解来分离纠缠的组分。此类策略仅显式提取如趋势等简单线性模式，而将其他线性模式及大量未探索的非线性模式留于残差中。其有缺陷的线性与非线性特征提取模型及浅层分解限制了它们对现实场景中多样化模式的适应能力。鉴于此，我们通过引入线性与非线性模式的显式提取，创新性地提出递归残差分解。这一更深层的分解框架被命名为LiNo，它使用Li模块（可为移动平均核）捕获线性模式，并使用No模块（可为Transformer编码器）建模非线性模式。这两种模式的提取以交替递归方式进行。为充分发挥LiNo的潜力，我们将当前简单的线性模式提取器发展为通用的可学习自回归模型，并设计了一种能够处理所有必要非线性模式的新型No模块。值得注意的是，所提出的LiNo在单变量与多变量预测场景下的十三个真实世界基准测试中达到了最先进水平。实验表明，当前预测模型可通过这种先进的递归残差分解获得更稳健且精确的结果。我们希望这项工作能为设计更有效的预测模型提供见解。代码发布于以下仓库：https://github.com/Levi-Ackman/LiNo。