# FreDo: Frequency Domain-based Long-Term Time Series Forecasting

arXiv: https://arxiv.org/abs/2205.12301 · HTML: https://mlsanity.com/paper/2205.12301/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 15 of its 45 references that are in the map.
- First posted on arXiv 24 May 2022.

## Builds on (most cited first, 15 of 15)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Reformer: The Efficient Transformer](https://mlsanity.com/paper/2001.04451/) (2020)
- [An Empirical Evaluation of Generic Convolutional and Recurrent Networks for Sequence Modeling](https://mlsanity.com/paper/1803.01271/) (2018)
- [MLP-Mixer: An all-MLP Architecture for Vision](https://mlsanity.com/paper/2105.01601/) (2021)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Connecting the Dots: Multivariate Time Series Forecasting with Graph Neural Networks](https://mlsanity.com/paper/2005.11650/) (2020)
- [Adaptive Graph Convolutional Recurrent Network for Traffic Forecasting](https://mlsanity.com/paper/2007.02842/) (2020)
- [A Dual-Stage Attention-Based Recurrent Neural Network for Time Series Prediction](https://mlsanity.com/paper/1704.02971/) (2017)
- [Temporal Pattern Attention for Multivariate Time Series Forecasting](https://mlsanity.com/paper/1809.04206/) (2018)
- [Adjusting for Autocorrelated Errors in Neural Networks for Time Series](https://mlsanity.com/paper/2101.12578/) (2021)
- [Integrated Pre-Processing for Bayesian Nonlinear System Identification with Gaussian Processes](https://mlsanity.com/paper/1303.2912/) (2013)

## Built on by (most cited first, 6 of 6)

- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [First De-Trend then Attend: Rethinking Attention for Time-Series Forecasting](https://mlsanity.com/paper/2212.08151/) (2022)
- [Deep Learning based Forecasting: a case study from the online fashion industry](https://mlsanity.com/paper/2305.14406/) (2023)
- [TFDNet: Time-Frequency Enhanced Decomposed Network for Long-term Time Series Forecasting](https://mlsanity.com/paper/2308.13386/) (2023)
- [A Joint Time-frequency Domain Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2305.14649/) (2023)
- [FSMLP: Modelling Channel Dependencies With Simplex Theory Based Multi-Layer Perceptions In Frequency Domain](https://mlsanity.com/paper/2412.01654/) (2024)

## Abstract (arXiv)

The ability to forecast far into the future is highly beneficial to many applications, including but not limited to climatology, energy consumption, and logistics. However, due to noise or measurement error, it is questionable how far into the future one can reasonably predict. In this paper, we first mathematically show that due to error accumulation, sophisticated models might not outperform baseline models for long-term forecasting. To demonstrate, we show that a non-parametric baseline model based on periodicity can actually achieve comparable performance to a state-of-the-art Transformer-based model on various datasets. We further propose FreDo, a frequency domain-based neural network model that is built on top of the baseline model to enhance its performance and which greatly outperforms the state-of-the-art model. Finally, we validate that the frequency domain is indeed better by comparing univariate models trained in the frequency v.s. time domain.