# DEPTS: Deep Expansion Learning for Periodic Time Series Forecasting

arXiv: https://arxiv.org/abs/2203.07681 · HTML: https://mlsanity.com/paper/2203.07681/

## Key facts

- Cited by 29 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 34 references that are in the map.
- First posted on arXiv 15 Mar 2022.

## Builds on (most cited first, 9 of 9)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Deep Residual Learning for Image Recognition](https://mlsanity.com/paper/1512.03385/) (2015)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [N-BEATS: Neural basis expansion analysis for interpretable time series forecasting](https://mlsanity.com/paper/1905.10437/) (2019)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [sktime: A Unified Interface for Machine Learning with Time Series](https://mlsanity.com/paper/1909.07872/) (2019)
- [Deep Factors for Forecasting](https://mlsanity.com/paper/1905.12417/) (2019)
- [Joint Air Quality and Weather Prediction Based on Multi-Adversarial Spatiotemporal Networks](https://mlsanity.com/paper/2012.15037/) (2020)

## Built on by (most cited first, 29 of 29)

- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [CycleNet: Enhancing Time Series Forecasting through Modeling Periodic Patterns](https://mlsanity.com/paper/2409.18479/) (2024)
- [Dish-TS: A General Paradigm for Alleviating Distribution Shift in Time Series Forecasting](https://mlsanity.com/paper/2302.14829/) (2023)
- [Non-autoregressive Conditional Diffusion Models for Time Series Prediction](https://mlsanity.com/paper/2306.05043/) (2023)
- [SegRNN: Segment Recurrent Neural Network for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2308.11200/) (2023)
- [Frequency Adaptive Normalization For Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2409.20371/) (2024)
- [FilterNet: Harnessing Frequency Filters for Time Series Forecasting](https://mlsanity.com/paper/2411.01623/) (2024)
- [BasisFormer: Attention-based Time Series Forecasting with Learnable and Interpretable Basis](https://mlsanity.com/paper/2310.20496/) (2023)
- [A Survey on Deep Learning based Time Series Analysis with Frequency Transformation](https://mlsanity.com/paper/2302.02173/) (2023)
- [Retrieval-Augmented Diffusion Models for Time Series Forecasting](https://mlsanity.com/paper/2410.18712/) (2024)
- [The Rise of Diffusion Models in Time-Series Forecasting](https://mlsanity.com/paper/2401.03006/) (2024)
- [Parsimony or Capability? Decomposition Delivers Both in Long-term Time Series Forecasting](https://mlsanity.com/paper/2401.11929/) (2024)
- [FreEformer: Frequency Enhanced Transformer for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2501.13989/) (2025)
- [Estimating Treatment Effects from Irregular Time Series Observations with Hidden Confounders](https://mlsanity.com/paper/2303.02320/) (2023)
- [Deep Frequency Derivative Learning for Non-stationary Time Series Forecasting](https://mlsanity.com/paper/2407.00502/) (2024)
- [Time Series Analysis in Frequency Domain: A Survey of Open Challenges, Opportunities and Benchmarks](https://mlsanity.com/paper/2504.07099/) (2025)
- [Multi-Modality Spatio-Temporal Forecasting via Self-Supervised Learning](https://mlsanity.com/paper/2405.03255/) (2024)
- [Multi-Modal View Enhanced Large Vision Models for Long-Term Time Series Forecasting](https://mlsanity.com/paper/2505.24003/) (2025)
- [Distributional Drift Adaptation with Temporal Conditional Variational Autoencoder for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2209.00654/) (2022)
- [D-PAD: Deep-Shallow Multi-Frequency Patterns Disentangling for Time Series Forecasting](https://mlsanity.com/paper/2403.17814/) (2024)
- [Neural Functions for Learning Periodic Signal](https://mlsanity.com/paper/2506.09526/) (2025)
- [A unified framework for establishing the universal approximation of transformer-type architectures](https://mlsanity.com/paper/2506.23551/) (2025)
- [Long-term Time Series Forecasting based on Decomposition and Neural Ordinary Differential Equations](https://mlsanity.com/paper/2311.04522/) (2023)
- [Multi-View Neural Differential Equations for Continuous-Time Stream Data in Long-Term Traffic Forecasting](https://mlsanity.com/paper/2408.06445/) (2024)
- [DSTFView: Multi-View Cloud-Edge Workload Forecasting with Dual-Input Spatio-Temporal-Frequency Modeling](https://mlsanity.com/paper/2607.22565/) (2026)
- [Deterministic Prediction as Global Velocity: Flow Matching for Probabilistic Time-Series Forecast](https://mlsanity.com/paper/2610.18621/) (2026)

## Abstract (arXiv)

Periodic time series (PTS) forecasting plays a crucial role in a variety of industries to foster critical tasks, such as early warning, pre-planning, resource scheduling, etc. However, the complicated dependencies of the PTS signal on its inherent periodicity as well as the sophisticated composition of various periods hinder the performance of PTS forecasting. In this paper, we introduce a deep expansion learning framework, DEPTS, for PTS forecasting. DEPTS starts with a decoupled formulation by introducing the periodic state as a hidden variable, which stimulates us to make two dedicated modules to tackle the aforementioned two challenges. First, we develop an expansion module on top of residual learning to perform a layer-by-layer expansion of those complicated dependencies. Second, we introduce a periodicity module with a parameterized periodic function that holds sufficient capacity to capture diversified periods. Moreover, our two customized modules also have certain interpretable capabilities, such as attributing the forecasts to either local momenta or global periodicity and characterizing certain core periodic properties, e.g., amplitudes and frequencies. Extensive experiments on both synthetic data and real-world data demonstrate the effectiveness of DEPTS on handling PTS. In most cases, DEPTS achieves significant improvements over the best baseline. Specifically, the error reduction can even reach up to 20% for a few cases. Finally, all codes are publicly available.