LiNo: Advancing Recursive Residual Decomposition of Linear and Nonlinear Patterns for Robust Time Series Forecasting

ICLR 2025 Conference Submission1614 Authors

Keywords: Time Series Forecasting, Deep learning.

TL;DR: We propose LiNo, a framework offering better linear and nonlinear patterns decomposition in time series data to enhance forecasting accuracy and robustness.

Abstract:

Forecasting models are pivotal in a data-driven world with vast volumes of time series data that appear as a compound of vast $\textbf{Li}$near and $\textbf{No}$nlinear 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 $\textbf{LiNo}$, 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 anonymous repository: https://anonymous.4open.science/r/LiNo-8225/.

Primary Area: learning on time series and dynamical systems

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Submission Number: 1614