# Scaling Law for Time Series Forecasting

arXiv: https://arxiv.org/abs/2405.15124 · HTML: https://mlsanity.com/paper/2405.15124/

## Key facts

- Cited by 33 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 44 references that are in the map.
- First posted on arXiv 24 May 2024.

## Builds on (most cited first, 29 of 29)

- [PyTorch: An Imperative Style, High-Performance Deep Learning Library](https://mlsanity.com/paper/1912.01703/) (2019)
- [Scaling Laws for Neural Language Models](https://mlsanity.com/paper/2001.08361/) (2020)
- [Training Compute-Optimal Large Language Models](https://mlsanity.com/paper/2203.15556/) (2022)
- [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)
- [Scaling Vision Transformers](https://mlsanity.com/paper/2106.04560/) (2021)
- [iTransformer: Inverted Transformers Are Effective for Time Series Forecasting](https://mlsanity.com/paper/2310.06625/) (2023)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [Large Language Models Are Zero-Shot Time Series Forecasters](https://mlsanity.com/paper/2310.07820/) (2023)
- [Pay Attention to MLPs](https://mlsanity.com/paper/2105.08050/) (2021)
- [Explaining Neural Scaling Laws](https://mlsanity.com/paper/2102.06701/) (2021)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [TSMixer: An All-MLP Architecture for Time Series Forecasting](https://mlsanity.com/paper/2303.06053/) (2023)
- [FITS: Modeling Time Series with 10k Parameters](https://mlsanity.com/paper/2307.03756/) (2023)
- [Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting](https://mlsanity.com/paper/1905.03806/) (2019)
- [TimeGPT-1](https://mlsanity.com/paper/2310.03589/) (2023)
- [LLM4TS: Aligning Pre-Trained LLMs as Data-Efficient Time-Series Forecasters](https://mlsanity.com/paper/2308.08469/) (2023)
- [A Neural Scaling Law from the Dimension of the Data Manifold](https://mlsanity.com/paper/2004.10802/) (2020)
- [An Analysis of Linear Time Series Forecasting Models](https://mlsanity.com/paper/2403.14587/) (2024)
- [Scaling-laws for Large Time-series Models](https://mlsanity.com/paper/2405.13867/) (2024)
- [The Underlying Scaling Laws and Universal Statistical Structure of Complex Datasets](https://mlsanity.com/paper/2306.14975/) (2023)
- [Direct and indirect evidence of compression of word lengths. Zipf's law of abbreviation revisited](https://mlsanity.com/paper/2303.10128/) (2023)

## Built on by (most cited first, 30 of 33)

- [GIFT-Eval: A Benchmark For General Time Series Forecasting Model Evaluation](https://mlsanity.com/paper/2410.10393/) (2024)
- [Sundial: A Family of Highly Capable Time Series Foundation Models](https://mlsanity.com/paper/2502.00816/) (2025)
- [Time Series Modeling for Heart Rate Prediction: From ARIMA to Transformers](https://mlsanity.com/paper/2406.12199/) (2024)
- [Towards Neural Scaling Laws for Time Series Foundation Models](https://mlsanity.com/paper/2410.12360/) (2024)
- [Two Heads are Better Than One: Test-time Scaling of Multi-agent Collaborative Reasoning](https://mlsanity.com/paper/2504.09772/) (2025)
- [Aurora: Towards Universal Generative Multimodal Time Series Forecasting](https://mlsanity.com/paper/2509.22295/) (2025)
- [Timer-S1: A Billion-Scale Time Series Foundation Model with Serial Scaling](https://mlsanity.com/paper/2603.04791/) (2026)
- [SafetyRepro: Configuration-Conditional Rank Instability on Alignment Benchmarks](https://mlsanity.com/paper/2605.25492/) (2026)
- [Intrinsic Entropy of Context Length Scaling in LLMs](https://mlsanity.com/paper/2502.01481/) (2025)
- [RAM: Recover Any 3D Human Motion in-the-Wild](https://mlsanity.com/paper/2603.19929/) (2026)
- [Reasoning or Retrieval? A Study of Answer Attribution on Large Reasoning Models](https://mlsanity.com/paper/2509.24156/) (2025)
- [There are no Champions in Supervised Long-Term Time Series Forecasting](https://mlsanity.com/paper/2502.14045/) (2025)
- [Pre-Registering the Detectable Effect: A Paired-MDE Budget for 4-bit Quantization Benchmarks, with a Pilot Audit](https://mlsanity.com/paper/2605.28873/) (2026)
- [Not All Data are Good Labels: On the Self-supervised Labeling for Time Series Forecasting](https://mlsanity.com/paper/2502.14704/) (2025)
- [From Tokenizer Bias to Backbone Capability: A Controlled Study of LLMs for Time Series Forecasting](https://mlsanity.com/paper/2504.08818/) (2025)
- [Test-Time Efficient Pretrained Model Portfolios for Time Series Forecasting](https://mlsanity.com/paper/2510.06419/) (2025)
- [BenchHAR: Benchmarking Self-Supervised Learning for Generalizable Sensor-based Activity Recognition](https://mlsanity.com/paper/2605.08296/) (2026)
- [Domain Fusion Controllable Generalization for Cross-Domain Time Series Forecasting from Multi-Domain Integrated Distribution](https://mlsanity.com/paper/2412.03068/) (2024)
- [MM-STFlowNet: A Transportation Hub-Oriented Multi-Mode Passenger Flow Prediction Method via Spatial-Temporal Dynamic Graph Modeling](https://mlsanity.com/paper/2504.06325/) (2025)
- [HGTS-Former: Hierarchical HyperGraph Transformer for Multivariate Time Series Analysis](https://mlsanity.com/paper/2508.02411/) (2025)
- [Time Series Foundation Models for Process Model Forecasting](https://mlsanity.com/paper/2512.07624/) (2025)
- [Discrete Prototypical Memories for Federated Time Series Foundation Models](https://mlsanity.com/paper/2604.04475/) (2026)
- [Accurate and Efficient Multivariate Time Series Forecasting via Offline Clustering](https://mlsanity.com/paper/2505.05738/) (2025)
- [Towards Multi-Fidelity Scaling Laws of Neural Surrogates in CFD](https://mlsanity.com/paper/2511.01830/) (2025)
- [E2CAR: An Efficient 2D-CNN Framework for Real-Time EEG Artifact Removal on Edge Devices](https://mlsanity.com/paper/2602.09035/) (2026)
- [Grounding Multi-Hop Reasoning in Structural Causal Models via Group Relative Policy Optimization](https://mlsanity.com/paper/2605.01482/) (2026)
- [When Do Foundation Models Pay Off? A Break-Even Analysis of Pretrained Time Series Forecasters](https://mlsanity.com/paper/2607.04919/) (2026)
- [Learning Spatio-Temporal Foundation Models from Pure Synthetic Data](https://mlsanity.com/paper/2607.16251/) (2026)
- [When Does Retrieval Help Time-Series Forecasting?](https://mlsanity.com/paper/2609.20193/) (2026)
- [KiT: A Foundation Model for Financial Time-Series Forecasting using DiffusionTransformers](https://mlsanity.com/paper/2609.34507/) (2026)

## Abstract (arXiv)

Scaling law that rewards large datasets, complex models and enhanced data granularity has been observed in various fields of deep learning. Yet, studies on time series forecasting have cast doubt on scaling behaviors of deep learning methods for time series forecasting: while more training data improves performance, more capable models do not always outperform less capable models, and longer input horizons may hurt performance for some models. We propose a theory for scaling law for time series forecasting that can explain these seemingly abnormal behaviors. We take into account the impact of dataset size and model complexity, as well as time series data granularity, particularly focusing on the look-back horizon, an aspect that has been unexplored in previous theories. Furthermore, we empirically evaluate various models using a diverse set of time series forecasting datasets, which (1) verifies the validity of scaling law on dataset size and model complexity within the realm of time series forecasting, and (2) validates our theoretical framework, particularly regarding the influence of look back horizon. We hope our findings may inspire new models targeting time series forecasting datasets of limited size, as well as large foundational datasets and models for time series forecasting in future work. Code for our experiments has been made public at https://github.com/JingzheShi/ScalingLawForTimeSeriesForecasting.