# An Analysis of Linear Time Series Forecasting Models

arXiv: https://arxiv.org/abs/2403.14587 · HTML: https://mlsanity.com/paper/2403.14587/

## Key facts

- Cited by 41 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 19 references that are in the map.
- First posted on arXiv 21 Mar 2024.

## Builds on (most cited first, 7 of 7)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [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)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [How Does It Function? Characterizing Long-term Trends in Production Serverless Workloads](https://mlsanity.com/paper/2312.10127/) (2023)

## Built on by (most cited first, 30 of 41)

- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Scaling Law for Time Series Forecasting](https://mlsanity.com/paper/2405.15124/) (2024)
- [Temporal Query Network for Efficient Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.12917/) (2025)
- [Time-o1: Time-Series Forecasting Needs Transformed Label Alignment](https://mlsanity.com/paper/2505.17847/) (2025)
- [Intervention-Aware Forecasting: Breaking Historical Limits from a System Perspective](https://mlsanity.com/paper/2405.13522/) (2024)
- [Lightweight Online Adaption for Time Series Foundation Model Forecasts](https://mlsanity.com/paper/2502.12920/) (2025)
- [Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2506.23424/) (2025)
- [Performance of Zero-Shot Time Series Foundation Models on Cloud Data](https://mlsanity.com/paper/2502.12944/) (2025)
- [Chimera: Effectively Modeling Multivariate Time Series with 2-Dimensional State Space Models](https://mlsanity.com/paper/2406.04320/) (2024)
- [Understanding Why Large Language Models Can Be Ineffective in Time Series Analysis: The Impact of Modality Alignment](https://mlsanity.com/paper/2410.12326/) (2024)
- [POCO: Scalable Neural Forecasting through Population Conditioning](https://mlsanity.com/paper/2506.14957/) (2025)
- [TimeInf: Time Series Data Contribution via Influence Functions](https://mlsanity.com/paper/2407.15247/) (2024)
- [ReFocus: Reinforcing Mid-Frequency and Key-Frequency Modeling for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2502.16890/) (2025)
- [Towards Principled Test-Time Adaptation for Time Series Forecasting](https://mlsanity.com/paper/2605.17250/) (2026)
- [FTMixer: Frequency and Time Domain Representations Fusion for Time Series Modeling](https://mlsanity.com/paper/2405.15256/) (2024)
- [A Practical Approach to Causal Inference over Time](https://mlsanity.com/paper/2410.10502/) (2024)
- [Disentangled Parameter-Efficient Linear Model for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2411.17257/) (2024)
- [Augmented Invertible Koopman Autoencoder for long-term time series forecasting](https://mlsanity.com/paper/2503.12930/) (2025)
- [RDIT: Residual-based Diffusion Implicit Models for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2509.02341/) (2025)
- [LiNo: Advancing Recursive Residual Decomposition of Linear and Nonlinear Patterns for Robust Time Series Forecasting](https://mlsanity.com/paper/2410.17159/) (2024)
- [Series-to-Series Diffusion Bridge Model](https://mlsanity.com/paper/2411.04491/) (2024)
- [Real-time Calibration Model for Low-cost Sensor in Fine-grained Time series](https://mlsanity.com/paper/2412.20170/) (2024)
- [Super-Linear: A Lightweight Pretrained Mixture of Linear Experts for Time Series Forecasting](https://mlsanity.com/paper/2509.15105/) (2025)
- [Optimal Look-back Horizon for Time Series Forecasting in Federated Learning](https://mlsanity.com/paper/2511.12791/) (2025)
- [Adapting Time Series Foundation Models through Data Mixtures](https://mlsanity.com/paper/2603.02840/) (2026)
- [DTMamba : Dual Twin Mamba for Time Series Forecasting](https://mlsanity.com/paper/2405.07022/) (2024)
- [Inner-Instance Normalization for Time Series Forecasting](https://mlsanity.com/paper/2510.08657/) (2025)
- [How Good Can Linear Models Be for Time-Series Forecasting?](https://mlsanity.com/paper/2606.27282/) (2026)
- [ML-Based Bidding Price Prediction for Pay-As-Bid Ancillary Services Markets: A Use Case in the German Control Reserve Market](https://mlsanity.com/paper/2503.17214/) (2025)
- [Unlocking the Potential of Linear Networks for Irregular Multivariate Time Series Forecasting](https://mlsanity.com/paper/2505.00590/) (2025)

## Abstract (arXiv)

Despite their simplicity, linear models perform well at time series forecasting, even when pitted against deeper and more expensive models. A number of variations to the linear model have been proposed, often including some form of feature normalisation that improves model generalisation. In this paper we analyse the sets of functions expressible using these linear model architectures. In so doing we show that several popular variants of linear models for time series forecasting are equivalent and functionally indistinguishable from standard, unconstrained linear regression. We characterise the model classes for each linear variant. We demonstrate that each model can be reinterpreted as unconstrained linear regression over a suitably augmented feature set, and therefore admit closed-form solutions when using a mean-squared loss function. We provide experimental evidence that the models under inspection learn nearly identical solutions, and finally demonstrate that the simpler closed form solutions are superior forecasters across 72% of test settings.