# Revisiting Long-term Time Series Forecasting: An Investigation on Linear Mapping

arXiv: https://arxiv.org/abs/2305.10721 · HTML: https://mlsanity.com/paper/2305.10721/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 39 references that are in the map.
- First posted on arXiv 18 May 2023.

## Builds on (most cited first, 21 of 21)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Non-stationary Transformers: Exploring the Stationarity in Time Series Forecasting](https://mlsanity.com/paper/2205.14415/) (2022)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [ETSformer: Exponential Smoothing Transformers for Time-series Forecasting](https://mlsanity.com/paper/2202.01381/) (2022)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [CoST: Contrastive Learning of Disentangled Seasonal-Trend Representations for Time Series Forecasting](https://mlsanity.com/paper/2202.01575/) (2022)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Scaleformer: Iterative Multi-scale Refining Transformers for Time Series Forecasting](https://mlsanity.com/paper/2206.04038/) (2022)
- [MTS-Mixers: Multivariate Time Series Forecasting via Factorized Temporal and Channel Mixing](https://mlsanity.com/paper/2302.04501/) (2023)
- [First De-Trend then Attend: Rethinking Attention for Time-Series Forecasting](https://mlsanity.com/paper/2212.08151/) (2022)
- [Deep ReLU Networks Have Surprisingly Simple Polytopes](https://mlsanity.com/paper/2305.09145/) (2023)
- [Unwrapping All ReLU Networks](https://mlsanity.com/paper/2305.09424/) (2023)

## Built on by (most cited first, 11 of 11)

- [TimeXer: Empowering Transformers for Time Series Forecasting with Exogenous Variables](https://mlsanity.com/paper/2402.19072/) (2024)
- [Adaptive Multi-Scale Decomposition Framework for Time Series Forecasting](https://mlsanity.com/paper/2406.03751/) (2024)
- [LLM-Mixer: Multiscale Mixing in LLMs for Time Series Forecasting](https://mlsanity.com/paper/2410.11674/) (2024)
- [AutoHFormer: Efficient Hierarchical Autoregressive Transformer for Time Series Prediction](https://mlsanity.com/paper/2506.16001/) (2025)
- [Introducing Spectral Attention for Long-Range Dependency in Time Series Forecasting](https://mlsanity.com/paper/2410.20772/) (2024)
- [Dataset-Driven Channel Masks in Transformers for Multivariate Time Series](https://mlsanity.com/paper/2410.23222/) (2024)
- [EffiCANet: Efficient Time Series Forecasting with Convolutional Attention](https://mlsanity.com/paper/2411.04669/) (2024)
- [LeMoLE: LLM-Enhanced Mixture of Linear Experts for Time Series Forecasting](https://mlsanity.com/paper/2412.00053/) (2024)
- [A Lightweight Plug-in Gate for Transformer-Based Time-Series Forecasters](https://mlsanity.com/paper/2609.21044/) (2026)
- [From HL to H+L-1 Parameters: A Hankel-Toeplitz Forecaster for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2609.33984/) (2026)
- [RideBench: A Large-Scale Exogenous-Aware Benchmark for Ride-Hailing Time Series Forecasting](https://mlsanity.com/paper/2610.11164/) (2026)

## Abstract (arXiv)

Introduction: Long-term time series forecasting (LTSF) has gained significant attention in recent years. While various specialized designs exist for capturing temporal dependency, recent studies have shown that even a single linear layer can achieve competitive performance. This paper investigates the intrinsic effectiveness of recent LTSF approaches and reveals the critical role of affine mapping. Materials and methods: We conduct comprehensive experiments on both simulated and real-world datasets to analyze the components of state-of-the-art models. A theoretical analysis is provided to explain the working mechanisms of affine mapping in periodic signal forecasting. We evaluate the impact of reversible normalization and input horizon extension on model robustness. Results: We find that (1) affine mapping dominates forecasting performance across commonly utilized benchmarks, with models learning similar transition matrices from input to output; (2) affine mapping effectively captures periodic patterns but struggles with non-periodic signals or time series with varying periods across channels; (3) reversible normalization significantly enhances trend forecasting by transforming non-periodic trends into periodic-like patterns; (4) increasing input horizon improves performance on multi-channel data with different periods. Code is available at: urlhttps://github.com/plumprc/RTSF. Conclusions: Our findings provide theoretical and experimental insights into the working mechanisms of LTSF models, highlighting both the strengths and limitations of linear approaches. The results suggest that future model development should focus on handling cross-channel period variations and non-periodic components.