# Long-term Forecasting with TiDE: Time-series Dense Encoder

**Authors:** Abhimanyu Das, Weihao Kong, Andrew Leach, Rajat Sen, Rose Yu  
**arXiv:** [2304.08424](https://arxiv.org/abs/2304.08424)  
**Date:** 2023-04-17  
**Summary page:** https://www.summarizepaper.com/en/paper/2304.08424v1/

## Key points

- Simple linear models can outperform Transformer-based approaches in long-term time-series forecasting
- The authors propose TiDE, a Multi-layer Perceptron (MLP) based encoder-decoder model, to address the limitations of linear models
- TiDE combines the simplicity and speed of linear models with the ability to handle covariates and non-linear dependencies
- The simplest linear analogue of TiDE can achieve near optimal error rates for linear dynamical systems (LDS) under certain assumptions
- TiDE matches or outperforms previous approaches on long-term time-series forecasting benchmarks while being 5-10 times faster than the best Transformer-based model
- Prior research has focused on deep neural network models for long-term forecasting, such as LongTrans, Informer, Autoformer, FEDFormer, and Pyraformer
- DLinear and PatchTST have shown promising results by leveraging linear mappings and self-attention mechanisms
- The problem setting involves predicting future values based on historical data in long-term time series forecasting benchmarks
- TiDE encodes past time series data along with covariates using dense MLPs and decodes future time series data with covariates using dense MLPs
- TiDE offers a simple yet effective deep learning architecture for long term time series forecasting with superior performance compared to existing neural network models while maintaining computational efficiency.

## Summary

In recent work, it has been shown that simple linear models can outperform Transformer-based approaches in long-term time-series forecasting. To address the limitations of linear models in modeling non-linear dependencies and covariates, the authors propose a Multi-layer Perceptron (MLP) based encoder-decoder model called Time-series Dense Encoder (TiDE). TiDE combines the simplicity and speed of linear models with the ability to handle covariates and non-linear dependencies. The authors prove theoretically that the simplest linear analogue of their model can achieve near optimal error rates for linear dynamical systems (LDS) under certain assumptions. They also empirically demonstrate that their method can match or outperform previous approaches on popular long-term time-series forecasting benchmarks while being 5-10 times faster than the best Transformer-based model. In terms of related work, prior research has focused on deep neural network models for long-term forecasting such as LongTrans, Informer, Autoformer, FEDFormer and Pyraformer which employ different mechanisms to capture temporal dependencies. Recently, DLinear and PatchTST have shown promising results by leveraging linear mappings and self-attention mechanisms. The problem setting involves long-term time series forecasting benchmarks where the goal is to predict future values based on historical data. The authors propose TiDE as a solution that encodes past time series data along with covariates using dense MLPs and decodes future time series data with covariates using dense MLPs. Overall, the proposed TiDE model offers a simple yet effective deep learning architecture for long term time series forecasting which achieves superior performance compared to existing neural network models while maintaining computational efficiency.