# Think Globally, Act Locally: A Deep Neural Network Approach to High-Dimensional Time Series Forecasting

arXiv: https://arxiv.org/abs/1905.03806 · HTML: https://mlsanity.com/paper/1905.03806/

## Key facts

- Cited by 161 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 May 2019.

## Built on by (most cited first, 30 of 161)

- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [FEDformer: Frequency Enhanced Decomposed Transformer for Long-term Series Forecasting](https://mlsanity.com/paper/2201.12740/) (2022)
- [A decoder-only foundation model for time-series forecasting](https://mlsanity.com/paper/2310.10688/) (2023)
- [SCINet: Time Series Modeling and Forecasting with Sample Convolution and Interaction](https://mlsanity.com/paper/2106.09305/) (2021)
- [Spectral Temporal Graph Neural Network for Multivariate Time-series Forecasting](https://mlsanity.com/paper/2103.07719/) (2021)
- [Time-MoE: Billion-Scale Time Series Foundation Models with Mixture of Experts](https://mlsanity.com/paper/2409.16040/) (2024)
- [Monash Time Series Forecasting Archive](https://mlsanity.com/paper/2105.06643/) (2021)
- [Deep Time Series Models: A Comprehensive Survey and Benchmark](https://mlsanity.com/paper/2407.13278/) (2024)
- [Frequency-domain MLPs are More Effective Learners in Time Series Forecasting](https://mlsanity.com/paper/2311.06184/) (2023)
- [FiLM: Frequency improved Legendre Memory Model for Long-term Time Series Forecasting](https://mlsanity.com/paper/2205.08897/) (2022)
- [FourierGNN: Rethinking Multivariate Time Series Forecasting from a Pure Graph Perspective](https://mlsanity.com/paper/2311.06190/) (2023)
- [AdaRNN: Adaptive Learning and Forecasting of Time Series](https://mlsanity.com/paper/2108.04443/) (2021)
- [Pathformer: Multi-scale Transformers with Adaptive Pathways for Time Series Forecasting](https://mlsanity.com/paper/2402.05956/) (2024)
- [Generative Time Series Forecasting with Diffusion, Denoise, and Disentanglement](https://mlsanity.com/paper/2301.03028/) (2023)
- [OneNet: Enhancing Time Series Forecasting Models under Concept Drift by Online Ensembling](https://mlsanity.com/paper/2309.12659/) (2023)
- [Domain Adaptation for Time Series Forecasting via Attention Sharing](https://mlsanity.com/paper/2102.06828/) (2021)
- [CARD: Channel Aligned Robust Blend Transformer for Time Series Forecasting](https://mlsanity.com/paper/2305.12095/) (2023)
- [A Survey on Time-Series Pre-Trained Models](https://mlsanity.com/paper/2305.10716/) (2023)
- [Do We Really Need Deep Learning Models for Time Series Forecasting?](https://mlsanity.com/paper/2101.02118/) (2021)
- [SAMformer: Unlocking the Potential of Transformers in Time Series Forecasting with Sharpness-Aware Minimization and Channel-Wise Attention](https://mlsanity.com/paper/2402.10198/) (2024)
- [Multi-resolution Time-Series Transformer for Long-term Forecasting](https://mlsanity.com/paper/2311.04147/) (2023)
- [Koopman Neural Forecaster for Time Series with Temporal Distribution Shifts](https://mlsanity.com/paper/2210.03675/) (2022)
- [Taming Local Effects in Graph-based Spatiotemporal Forecasting](https://mlsanity.com/paper/2302.04071/) (2023)
- [Temporal Knowledge Graph Forecasting Without Knowledge Using In-Context Learning](https://mlsanity.com/paper/2305.10613/) (2023)
- [From Similarity to Superiority: Channel Clustering for Time Series Forecasting](https://mlsanity.com/paper/2404.01340/) (2024)
- [Learning the Evolutionary and Multi-scale Graph Structure for Multivariate Time Series Forecasting](https://mlsanity.com/paper/2206.13816/) (2022)
- [Low-Rank Autoregressive Tensor Completion for Spatiotemporal Traffic Data Imputation](https://mlsanity.com/paper/2104.14936/) (2021)
- [In-Context Fine-Tuning for Time-Series Foundation Models](https://mlsanity.com/paper/2410.24087/) (2024)
- [Missing Value Imputation on Multidimensional Time Series](https://mlsanity.com/paper/2103.01600/) (2021)
- [Scaling Law for Time Series Forecasting](https://mlsanity.com/paper/2405.15124/) (2024)

## Abstract (arXiv)

Forecasting high-dimensional time series plays a crucial role in many applications such as demand forecasting and financial predictions. Modern datasets can have millions of correlated time-series that evolve together, i.e they are extremely high dimensional (one dimension for each individual time-series). There is a need for exploiting global patterns and coupling them with local calibration for better prediction. However, most recent deep learning approaches in the literature are one-dimensional, i.e, even though they are trained on the whole dataset, during prediction, the future forecast for a single dimension mainly depends on past values from the same dimension. In this paper, we seek to correct this deficiency and propose DeepGLO, a deep forecasting model which thinks globally and acts locally. In particular, DeepGLO is a hybrid model that combines a global matrix factorization model regularized by a temporal convolution network, along with another temporal network that can capture local properties of each time-series and associated covariates. Our model can be trained effectively on high-dimensional but diverse time series, where different time series can have vastly different scales, without a priori normalization or rescaling. Empirical results demonstrate that DeepGLO can outperform state-of-the-art approaches; for example, we see more than 25% improvement in WAPE over other methods on a public dataset that contains more than 100K-dimensional time series.