A Time Series is Worth 64 Words: Long-term Forecasting with Transformers

2022/11/27 by Yuqi Nie, Nie, Yuqi, Nam Hoai Nguyen +5 · 600 citations
Computer Science · Decision Sciences · #Anomaly Detection Techniques and Applications #Artificial Intelligence (cs.AI) #FOS: Computer and information sciences #Machine Learning (cs.LG) #Stock Market Forecasting Methods #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2211.14730

openalex publication_date 2022/11/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/31

Abstract

We propose an efficient design of Transformer-based models for multivariate time series forecasting and self-supervised representation learning. It is based on two key components: (i) segmentation of time series into subseries-level patches which are served as input tokens to Transformer; (ii) channel-independence where each channel contains a single univariate time series that shares the same embedding and Transformer weights across all the series. Patching design naturally has three-fold benefit: local semantic information is retained in the embedding; computation and memory usage of the attention maps are quadratically reduced given the same look-back window; and the model can attend longer history. Our channel-independent patch time series Transformer (PatchTST) can improve the long-term forecasting accuracy significantly when compared with that of SOTA Transformer-based models. We also apply our model to self-supervised pre-training tasks and attain excellent fine-tuning performance, which outperforms supervised training on large datasets. Transferring of masked pre-trained representation on one dataset to others also produces SOTA forecasting accuracy. Code is available at: https://github.com/yuqinie98/PatchTST.

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• Towards Robust Real-World Multivariate Time Series Forecasting: A Unified Framework for Dependency, Asynchrony, and Missingness
• Time Series Representations for Classification Lie Hidden in Pretrained Vision Transformers
• MD-ViSCo: A Unified Model for Multi-Directional Vital Sign Waveform Conversion
• KARMA: A Multilevel Decomposition Hybrid Mamba Framework for Multivariate Long-Term Time Series Forecasting
• A Comprehensive Benchmark for Electrocardiogram Time-Series
• Data Augmentation in Time Series Forecasting through Inverted Framework
• EEG Foundation Models: A Critical Review of Current Progress and Future Directions
• StellarF: A Physics-Informed LoRA Framework for Stellar Flare Forecasting with Historical & Statistical Data
• Fusing Large Language Models with Temporal Transformers for Time Series Forecasting
• Reprogramming Vision Foundation Models for Spatio-Temporal Forecasting
• TRACE: Grounding Time Series in Context for Multimodal Embedding and Retrieval
• TAT: Temporal-Aligned Transformer for Multi-Horizon Peak Demand Forecasting
• NeuTSFlow: Modeling Continuous Functions Behind Time Series Forecasting
• Deformable Dynamic Convolution for Accurate yet Efficient Spatio-Temporal Traffic Prediction
• Fourier Basis Mapping: A Time-Frequency Learning Framework for Time Series Forecasting
• TFGformer: Multivariate Time Series Forecasting via Time-Frequency Graph Learning and Covariate Fusion
• Bridging the Last Mile of Prediction: Enhancing Time Series Forecasting with Conditional Guided Flow Matching
• Foundation models for time series forecasting: Application in conformal prediction
• MoFE-Time: Mixture of Frequency Domain Experts for Time-Series Forecasting Models
• DiffSpectra: Molecular Structure Elucidation from Spectra using Diffusion Models
• One task to rule them all: A closer look at traffic classification generalizability
• Decomposing the Time Series Forecasting Pipeline: A Modular Approach for Time Series Representation, Information Extraction, and Projection
• A Wireless Foundation Model for Multi-Task Prediction
• DisMS-TS: Eliminating Redundant Multi-Scale Features for Time Series Classification
• Advancing Financial Engineering with Foundation Models: Progress, Applications, and Challenges
• DC-Mamber: A Dual Channel Prediction Model based on Mamba and Linear Transformer for Multivariate Time Series Forecasting
• Extreme Value Theory-based Distributed Interference Prediction for 6G Industrial Sub-networks
• LLM4Hint: Leveraging Large Language Models for Hint Recommendation in Offline Query Optimization
• Temporal Window Smoothing of Exogenous Variables for Improved Time Series Prediction
• TimeRFT: Stimulating Generalizable Time Series Forecasting for TSFMs via Reinforcement Finetuning
• Overtake Detection in Trucks Using CAN Bus Signals: A Comparative Study of Machine Learning Methods
• Evaluation of a Foundational Model and Stochastic Models for Forecasting Sporadic or Spiky Production Outages of High-Performance Machine Learning Services
• When Will It Fail?: Anomaly to Prompt for Forecasting Future Anomalies in Time Series
• Teaching Time Series to See and Speak: Forecasting with Aligned Visual and Textual Perspectives
• Accurate Parameter-Efficient Test-Time Adaptation for Time Series Forecasting
• UniCA: Unified Covariate Adaptation for Time Series Foundation Model
• Time Series Continuous Modeling for Imputation and Forecasting with Implicit Neural Representations
• Masked Autoencoders that Feel the Heart: Unveiling Simplicity Bias for ECG Analyses
• SEED: A Structural Encoder for Embedding-Driven Decoding in Time Series Prediction with LLMs
• Echo State Transformer: Attention Over Finite Memories
• ITFormer: Bridging Time Series and Natural Language for Multi-Modal QA with Large-Scale Multitask Dataset
• FAF: A Feature-Adaptive Framework for Few-Shot Time Series Forecasting
• Scaling Transformers for Time Series Forecasting: Do Pretrained Large Models Outperform Small-Scale Alternatives?
• TAB: Unified Benchmarking of Time Series Anomaly Detection Methods
• Damba-ST: Domain-Adaptive Mamba for Efficient Urban Spatio-Temporal Prediction
• Time-Prompt: Integrated Heterogeneous Prompts for Unlocking LLMs in Time Series Forecasting
• When Does Multimodality Lead to Better Time Series Forecasting?
• Cross-Modal Epileptic Signal Harmonization: Frequency Domain Mapping Quantization for Pre-training a Unified Neurophysiological Transformer
• Biaxialformer: Leveraging Channel Independence and Inter-Channel Correlations in EEG Signal Decoding for Predicting Neurological Outcomes
• MIRA: Medical Time Series Foundation Model for Real-World Health Data
• Human Locomotion Implicit Modeling Based Real-Time Gait Phase Estimation
• Enhancing Spatio-Temporal Forecasting with Spatial Neighbourhood Fusion:A Case Study on COVID-19 Mobility in Peru
• Deep learning forecasts the spatiotemporal evolution of fluid-induced microearthquakes
• SKOLR: Structured Koopman Operator Linear RNN for Time-Series Forecasting
• Multi-Scale Finetuning for Encoder-based Time Series Foundation Models
• Leveraging External Factors in Household-Level Electrical Consumption Forecasting using Hypernetworks
• CoIFNet: A Unified Framework for Multivariate Time Series Forecasting with Missing Values
• TimeMaster: Training Time-Series Multimodal LLMs to Reason via Reinforcement Learning
• Forecast-Then-Optimize Deep Learning Methods
• A Review of the Long Horizon Forecasting Problem in Time Series Analysis
• TFKAN: Time-Frequency KAN for Long-Term Time Series Forecasting
• Forecasting Time Series with LLMs via Patch-Based Prompting and Decomposition
• MetaEformer: Unveiling and Leveraging Meta-patterns for Complex and Dynamic Systems Load Forecasting
• Delayformer: spatiotemporal transformation for predicting high-dimensional dynamics
• ST-MTM: Masked Time Series Modeling with Seasonal-Trend Decomposition for Time Series Forecasting
• A hybrid dual-branch model with recurrence plots and transposed transformer for stock trend prediction
• PromptTSS: A Prompting-Based Approach for Interactive Multi-Granularity Time Series Segmentation
• Time Series Forecasting as Reasoning: A Slow-Thinking Approach with Reinforced LLMs
• PhysioWave: A Multi-Scale Wavelet-Transformer for Physiological Signal Representation
• Time-IMM: A Dataset and Benchmark for Irregular Multimodal Multivariate Time Series
• LightGTS: A Lightweight General Time Series Forecasting Model
• Comparative Analysis of Modern Machine Learning Models for Retail Sales Forecasting
• NILMFormer: Non-Intrusive Load Monitoring that Accounts for Non-Stationarity
• LETS Forecast: Learning Embedology for Time Series Forecasting
• TimeRecipe: A Time-Series Forecasting Recipe via Benchmarking Module Level Effectiveness
• LSM-2: Learning from Incomplete Wearable Sensor Data
• FaCTR: Factorized Channel-Temporal Representation Transformers for Efficient Time Series Forecasting
• ALFEE: Adaptive Large Foundation Model for EEG Representation
• Retrieval Augmented Time Series Forecasting
• Non-stationary Diffusion For Probabilistic Time Series Forecasting
• STRGCN: Capturing Asynchronous Spatio-Temporal Dependencies for Irregular Multivariate Time Series Forecasting
• Uncovering Insights of Compound Flooding with Data-Driven AI
• Intelligent Routing for Sparse Demand Forecasting: A Comparative Evaluation of Selection Strategies
• CHIME: Conditional Hallucination and Integrated Multi-scale Enhancement for Time Series Diffusion Model
• Temporal horizons in forecasting: a performance-learnability trade-off
• Zero-Shot Time Series Forecasting with Covariates via In-Context Learning
• XicorAttention: Time Series Transformer Using Attention with Nonlinear Correlation
• Temporal Variational Implicit Neural Representations
• Rating Quality of Diverse Time Series Data by Meta-learning from LLM Judgment
• MoCA: Multi-modal Cross-masked Autoencoder for Time Series in Digital Health
• HouseTS: A Large-Scale, Multimodal Spatiotemporal U.S. Housing Dataset and Benchmark
• Enhancing LLM Reasoning for Time Series Classification by Tailored Thinking and Fused Decision
• A Dynamic Stiefel Graph Neural Network for Efficient Spatio-Temporal Time Series Forecasting
• Learning with Calibration: Exploring Test-Time Computing of Spatio-Temporal Forecasting
• Predictability-Aware Compression and Decompression Framework for Multichannel Time Series Data
• Revisiting LLMs as Zero-Shot Time-Series Forecasters: Small Noise Can Break Large Models
• Channel Normalization for Time Series Channel Identification
• Channel-Imposed Fusion: A Simple yet Effective Method for Medical Time Series Classification
• Can LLMs Understand Unvoiced Speech? Exploring EMG-to-Text Conversion with LLMs
• Timing is Important: Risk-aware Fund Allocation based on Time-Series Forecasting
• Can Slow-thinking LLMs Reason Over Time? Empirical Studies in Time Series Forecasting
• CrossLinear: Plug-and-Play Cross-Correlation Embedding for Time Series Forecasting with Exogenous Variables
• K²VAE: A Koopman-Kalman Enhanced Variational AutoEncoder for Probabilistic Time Series Forecasting
• Non-collective Calibrating Strategy for Time Series Forecasting
• Improving Time Series Forecasting via Instance-aware Post-hoc Revision
• TiRex: Zero-Shot Forecasting Across Long and Short Horizons with Enhanced In-Context Learning
• Mamba Integrated with Physics Principles Masters Long-term Chaotic System Forecasting
• Multi-Modal View Enhanced Large Vision Models for Long-Term Time Series Forecasting
• From Images to Signals: Are Large Vision Models Useful for Time Series Analysis?
• IMTS is Worth Time × Channel Patches: Visual Masked Autoencoders for Irregular Multivariate Time Series Prediction
• Self-supervised Learning Method Using Transformer for Multi-dimensional Sensor Data Processing
• Multimodal Forecasting of Sparse Intraoperative Hypotension Events Powered by Language Model
• Multivariate de Bruijn Graphs: A Symbolic Graph Framework for Time Series Forecasting
• Forecasting Multivariate Urban Data via Decomposition and Spatio-Temporal Graph Analysis
• UDuo: Universal Dual Optimization Framework for Online Matching
• Continuous Evolution Pool: Taming Recurring Concept Drift in Online Time Series Forecasting
• CSI-Bench: A Large-Scale In-the-Wild Dataset for Multi-task WiFi Sensing
• TimePro: Efficient Multivariate Long-term Time Series Forecasting with Variable- and Time-Aware Hyper-state
• PIPE: Physics-Informed Position Encoding for Alignment of Satellite Images and Time Series
• AutoReproduce: Automatic AI Experiment Reproduction with Paper Lineage
• Are Data Embeddings effective in time series forecasting?
• SCFormer: Structured Channel-wise Transformer with Cumulative Historical State for Multivariate Time Series Forecasting
• Synthetic Time Series Forecasting with Transformer Architectures: Extensive Simulation Benchmarks
• Gradient Flow Matching for Learning Update Dynamics in Neural Network Training
• A Unified Foundation Model for Wireless Technology Recognition and Localization
• Beyond Fixed Patches: Enhancing GPTs for Financial Prediction with Adaptive Segmentation and Learnable Wavelets
• CMoS: Rethinking Time Series Prediction Through the Lens of Chunk-wise Spatial Correlations
• Multi-Source Dynamic Graph Learning for Compound-Flood Forecasting in Managed Coastal Systems
• Latent-Regime Bias Auditing for Volatility Forecasting
• Breaking Silos: Adaptive Model Fusion Unlocks Better Time Series Forecasting
• CARE: A Cascaded Framework for Efficient and Reliable Time Series Anomaly Detection
• BLAST: Balanced Sampling Time Series Corpus for Universal Forecasting Models
• Causal Spatio-Temporal Prediction: An Effective and Efficient Multi-Modal Approach
• TimeCF: A TimeMixer-Based Model with adaptive Convolution and Sharpness-Aware Minimization Frequency Domain Loss for long-term time seris forecasting
• HyperIMTS: Hypergraph Neural Network for Irregular Multivariate Time Series Forecasting
• Time-o1: Time-Series Forecasting Needs Transformed Label Alignment
• Mixture of Low Rank Adaptation with Partial Parameter Sharing for Time Series Forecasting
• Ellipsoidal Time Series Forecasting
• GLAIM: Learning Global and Local Adaptive Inter-Variable Dependency for Multivariate Time Series Imputation
• FlowMixer: A Constrained Neural Architecture for Interpretable Spatiotemporal Forecasting
• Beyond All-to-All: Causal-Aligned Transformer with Dynamic Structure Learning for Multivariate Time Series Forecasting
• When can isotropy help adapt LLMs' next word prediction to numerical domains?
• From Local Patterns to Global Understanding: Cross-Stock Trend Integration for Enhanced Predictive Modeling
• Human in the Loop Adaptive Optimization for Improved Time Series Forecasting
• Time Tracker: Mixture-of-Experts-Enhanced Foundation Time Series Forecasting Model with Decoupled Training Pipelines
• Beyond Magnitude and Shape: A Direction-Aware Loss for Time Series Forecasting
• Large Language models for Time Series Analysis: Techniques, Applications, and Challenges
• R&D-Agent-Quant: A Multi-Agent Framework for Data-Centric Factors and Model Joint Optimization
• Evaluating Forecasting Techniques for Hardware Errors on a Large-scale HPC System
• MoTime: A Dataset Suite for Multimodal Time Series Forecasting
• Sonnet: Spectral Operator Neural Network for Multivariable Time Series Forecasting
• Byte Pair Encoding for Efficient Time Series Forecasting
• CRAFT: Time Series Forecasting with Cross-Future Behavior Awareness
• Leveraging Multivariate Long-Term History Representation for Time Series Forecasting
• Output Scaling: YingLong-Delayed Chain of Thought in a Large Pretrained Time Series Forecasting Model
• Time to Embed: Unlocking Foundation Models for Time Series with Channel Descriptions
• This Time is Different: An Observability Perspective on Time Series Foundation Models
• FlowBERT: Prompt-tuned BERT for variable flow field prediction
• TSPulse: Tiny Pre-Trained Models with Disentangled Representations for Rapid Time-Series Analysis
• CATS: Clustering-Aggregated and Time Series for Business Customer Purchase Intention Prediction
• Enhancing Channel-Independent Time Series Forecasting via Cross-Variate Patch Embedding
• Temporal Query Network for Efficient Multivariate Time Series Forecasting
• Enhancing LLMs for Time Series Forecasting via Structure-Guided Cross-Modal Alignment
• Zero-Shot Forecasting Mortality Rates: A Global Study
• Multi-Order Wavelet Derivative Transform for Deep Time Series Forecasting
• Nearest Neighbor Multivariate Time Series Forecasting
• Context-Aware Probabilistic Modeling with LLM for Multimodal Time Series Forecasting
• OLMA: One Loss for More Accurate Time Series Forecasting
• Logo-LLM: Local and Global Modeling with Large Language Models for Time Series Forecasting
• Foundation Time-Series AI Model for Realized Volatility Forecasting
• Rethinking Irregular Time Series Forecasting: A Simple yet Effective Baseline
• ChronoSteer: Bridging Large Language Model and Time Series Foundation Model via Synthetic Data
• An Efficient deep learning model to Predict Stock Price Movement Based on Limit Order Book
• TRACE-TS: Attribution-Grounded and Traceable Sensor-Language Reasoning for Human Activity Understanding
• Block-Biased Mamba for Long-Range Sequence Processing
• SPAT: Sensitivity-based Multihead-attention Pruning on Time Series Forecasting Models
• A Multi-scale Representation Learning Framework for Long-Term Time Series Forecasting
• DELPHYNE: A Pre-Trained Model for General and Financial Time Series
• A Comparative Study of Transformer-Based Models for Multi-Horizon Blood Glucose Prediction
• OLinear: A Linear Model for Time Series Forecasting in Orthogonally Transformed Domain
• Learning Soft Sparse Shapes for Efficient Time-Series Classification
• Sparse Latent Factor Forecaster (SLFF) with Iterative Inference for Transparent Multi-Horizon Commodity Futures Prediction
• Mixer-Informer-Based Two-Stage Transfer Learning for Long-Sequence Load Forecasting in Newly Constructed Electric Vehicle Charging Stations
• Accurate and Efficient Multivariate Time Series Forecasting via Offline Clustering
• FIC-TSC: Learning Time Series Classification with Fisher Information Constraint
• Generalization Analysis for Supervised Contrastive Representation Learning under Non-IID Settings
• Cardioformer: Advancing AI in ECG Analysis with Multi-Granularity Patching and ResNet
• AROpt: An Optimization Method for Autoregressive Time Series Forecasting
• CASA: CNN Autoencoder-based Score Attention for Efficient Multivariate Long-term Time-series Forecasting
• Efficient Multivariate Time Series Forecasting via Calibrated Language Models with Privileged Knowledge Distillation
• How Effective are Large Time Series Models in Hydrology? A Study on Water Level Forecasting in Everglades
• Dual-Forecaster: A Multimodal Time Series Model Integrating Descriptive and Predictive Texts
• Pretrained Time-Series Foundation Models for Financial Return Forecasting
• Unlocking the Potential of Linear Networks for Irregular Multivariate Time Series Forecasting
• Deep Learning for Financial Time Series: A Large-Scale Benchmark of Risk-Adjusted Performance
• Visual Reasoning over Time Series via Multi-Agent System
• Sedentary Behavior Classification for Wearable Sensors with a CNN-BiLSTM Model
• Simulation as Supervision: Mechanistic Pretraining for Scientific Discovery
• Gateformer: Advancing Multivariate Time Series Forecasting through Temporal and Variate-Wise Attention with Gated Representations
• Prediction of Solar Flares Using Photospheric Magnetic Field Parameters with Deep Learning
• APEX: A Network-Native Time-Series Foundation Model for Forecasting and Anomaly Detection for Wireless Edge Operations
• Generalized Stock Price Prediction for Multiple Stocks Combined with News Fusion
• FinStressTS: A Parametric Synthetic Benchmark for Time-Series Forecasting in Finance
• NPMixer: Hierarchical Neighboring Patch Mixing for Time Series Forecasting
• Financially Guided Deep Portfolio Optimization
• TopoPrimer: The Missing Topological Context in Forecasting Models
• A Market-Rule-Informed Neural Network for Efficient Imbalance Electricity Price Forecasting
• TAMO: Fine-Grained Root Cause Analysis via Tool-Assisted LLM Agent with Multi-Modality Observation Data in Cloud-Native Systems
• Pretraining Large Brain Language Model for Active BCI: Silent Speech
• Multimodal Conditioned Diffusive Time Series Forecasting
• TimeSAE: Causal Sparse Decoding for Faithful Explanations of Black-Box Time Series Models
• TSRM: A Lightweight Temporal Feature Encoding Architecture for Time Series Forecasting and Imputation
• Behavior Score Prediction in Resting-State Functional MRI by Deep State Space Modeling
• CalM: A Self-Supervised Foundation Model for Population Dynamics in Calcium Imaging Data
• Test-Time Adaptation for Non-stationary Time Series: From Synthetic Regime Shifts to Financial Markets
• DeePM: Regime-Robust Deep Learning for Systematic Macro Portfolio Management
• Smart Predict--then--Optimize Paradigm for Portfolio Optimization in Real Markets
• QuantBench: Benchmarking AI Methods for Quantitative Investment
• FinVerse: Financial Time-Series Benchmark
• A Simple Review of EEG Foundation Models: Datasets, Advancements and Future Perspectives
• ExOSITO: Explainable Off-Policy Learning with Side Information for Intensive Care Unit Blood Test Orders
• Tokenizing Stock Prices for Enhanced Multi-Step Forecast and Prediction
• CANet: ChronoAdaptive Network for Enhanced Long-Term Time Series Forecasting under Non-Stationarity
• Goal-Oriented Time-Series Forecasting: Foundation Framework Design
• Improving Significant Wave Height Prediction Using Chronos Models
• Beyond Linear Dynamics: Neural Bilinear Dynamical Models for Time Series Forecasting
• CAMP: A Cycle-Aware Multi-Scale Patch Mixer for Time Series Forecasting
• Transformer representation learning is necessary for dynamic multi-modal physiological data on small-cohort patients
• iTFKAN: Interpretable Time Series Forecasting with Kolmogorov-Arnold Network
• Evaluating Temporal Plasticity in Foundation Time Series Models for Incremental Fine-tuning
• A Physics-guided Multimodal Transformer Path to Weather and Climate Sciences
• Energy-Aware Pattern Disentanglement: A Generalizable Pattern Assisted Architecture for Multi-task Time Series Analysis
• PV-VLM: A Multimodal Vision-Language Approach Incorporating Sky Images for Intra-Hour Photovoltaic Power Forecasting
• A synthetic dataset of French electric load curves with temperature conditioning
• Foundation Models for Time Series: A Survey
• Multivariate Time Series Forecasting needs Cross Variable Loss
• Enhancing Anomaly Resilience in Research Networks: A Large-Scale Forecasting Benchmark for Dynamic Security Baselining
• MM-ISTS: Cooperating Irregularly Sampled Time Series Forecasting with Multimodal Vision-Text LLMs
• FISformer: Replacing Self-Attention with a Fuzzy Inference System in Transformer Models for Time Series Forecasting
• Bridging Distribution Gaps in Time Series Foundation Model Pretraining with Prototype-Guided Normalization
• Unleashing Expert Opinion from Social Media for Stock Prediction
• Air Quality Prediction with A Meteorology-Guided Modality-Decoupled Spatio-Temporal Network
• AimTS: Augmented Series and Image Contrastive Learning for Time Series Classification
• Can Competition Enhance the Proficiency of Agents Powered by Large Language Models in the Realm of News-driven Time Series Forecasting?
• ms-Mamba: Multi-scale Mamba for Time-Series Forecasting
• PatchTrAD: A Patch-Based Transformer focusing on Patch-Wise Reconstruction Error for Time Series Anomaly Detection
• Enhancing Time Series Forecasting via Multi-Level Text Alignment with LLMs
• Exploring the Effectiveness and Interpretability of Texts in LLM-based Time Series Models

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