# Stecformer: Spatio-temporal Encoding Cascaded Transformer for Multivariate Long-term Time Series Forecasting

arXiv: https://arxiv.org/abs/2305.16370 · HTML: https://mlsanity.com/paper/2305.16370/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 21 references that are in the map.
- First posted on arXiv 25 May 2023.

## Builds on (most cited first, 14 of 14)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [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)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [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)
- [Temporal Fusion Transformers for Interpretable Multi-horizon Time Series Forecasting](https://mlsanity.com/paper/1912.09363/) (2019)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [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)
- [Revisiting Spatial-Temporal Similarity: A Deep Learning Framework for Traffic Prediction](https://mlsanity.com/paper/1803.01254/) (2018)
- [Triformer: Triangular, Variable-Specific Attentions for Long Sequence Multivariate Time Series Forecasting--Full Version](https://mlsanity.com/paper/2204.13767/) (2022)

## Built on by (most cited first, 1 of 1)

- [Benchmarking M-LTSF: Frequency and Noise-Based Evaluation of Multivariate Long Time Series Forecasting Models](https://mlsanity.com/paper/2510.04900/) (2025)

## Abstract (arXiv)

Multivariate long-term time series forecasting is of great application across many domains, such as energy consumption and weather forecasting. With the development of transformer-based methods, the performance of multivariate long-term time series forecasting has been significantly improved, however, the study of spatial features extracting in transformer-based model is rare and the consistency of different prediction periods is unsatisfactory due to the large span. In this work, we propose a complete solution to address these problems in terms of feature extraction and target prediction. For extraction, we design an efficient spatio-temporal encoding extractor including a semi-adaptive graph to acquire sufficient spatio-temporal information. For prediction, we propose a Cascaded Decoding Predictor (CDP) to strengthen the correlation between different intervals, which can also be utilized as a generic component to improve the performance of transformer-based methods. The proposed method, termed as Spatio-temporal Encoding Cascaded Transformer (Stecformer), achieving a notable gap over the baseline model and is comparable with the state-of-the-art performance of transformer-based methods on five benchmark datasets. We hope our attempt will serve as a regular configuration in multivariate long-term time series forecasting in the future.