# Efficient Multivariate Time Series Forecasting via Calibrated Language Models with Privileged Knowledge Distillation

arXiv: https://arxiv.org/abs/2505.02138 · HTML: https://mlsanity.com/paper/2505.02138/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- Placed in General knowledge distillation methods, one of 12 directions in Knowledge distillation.
- Builds on 35 of its 63 references that are in the map.
- First posted on arXiv 4 May 2025.

## Placed in

- Knowledge distillation / [General knowledge distillation methods](https://mlsanity.com/distill/general-knowledge-distillation-methods/)

## Builds on (most cited first, 30 of 35)

- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [A Time Series is Worth 64 Words: Long-term Forecasting with Transformers](https://mlsanity.com/paper/2211.14730/) (2022)
- [Autoformer: Decomposition Transformers with Auto-Correlation for Long-Term Series Forecasting](https://mlsanity.com/paper/2106.13008/) (2021)
- [Knowledge Distillation: A Survey](https://mlsanity.com/paper/2006.05525/) (2020)
- [Are Transformers Effective for Time Series Forecasting?](https://mlsanity.com/paper/2205.13504/) (2022)
- [TimesNet: Temporal 2D-Variation Modeling for General Time Series Analysis](https://mlsanity.com/paper/2210.02186/) (2022)
- [On Layer Normalization in the Transformer Architecture](https://mlsanity.com/paper/2002.04745/) (2020)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Time-LLM: Time Series Forecasting by Reprogramming Large Language Models](https://mlsanity.com/paper/2310.01728/) (2023)
- [One Fits All:Power General Time Series Analysis by Pretrained LM](https://mlsanity.com/paper/2302.11939/) (2023)
- [TFB: Towards Comprehensive and Fair Benchmarking of Time Series Forecasting Methods](https://mlsanity.com/paper/2403.20150/) (2024)
- [Foundation Models for Time Series Analysis: A Tutorial and Survey](https://mlsanity.com/paper/2403.14735/) (2024)
- [Unifying distillation and privileged information](https://mlsanity.com/paper/1511.03643/) (2015)
- [TEMPO: Prompt-based Generative Pre-trained Transformer for Time Series Forecasting](https://mlsanity.com/paper/2310.04948/) (2023)
- [PromptCast: A New Prompt-based Learning Paradigm for Time Series Forecasting](https://mlsanity.com/paper/2210.08964/) (2022)
- [TEST: Text Prototype Aligned Embedding to Activate LLM's Ability for Time Series](https://mlsanity.com/paper/2308.08241/) (2023)
- [UniTime: A Language-Empowered Unified Model for Cross-Domain Time Series Forecasting](https://mlsanity.com/paper/2310.09751/) (2023)
- [Exploring Progress in Multivariate Time Series Forecasting: Comprehensive Benchmarking and Heterogeneity Analysis](https://mlsanity.com/paper/2310.06119/) (2023)
- [CALF: Aligning LLMs for Time Series Forecasting via Cross-modal Fine-Tuning](https://mlsanity.com/paper/2403.07300/) (2024)
- [TimeCMA: Towards LLM-Empowered Multivariate Time Series Forecasting via Cross-Modality Alignment](https://mlsanity.com/paper/2406.01638/) (2024)
- [Spatial-Temporal Large Language Model for Traffic Prediction](https://mlsanity.com/paper/2401.10134/) (2024)
- [AutoTimes: Autoregressive Time Series Forecasters via Large Language Models](https://mlsanity.com/paper/2402.02370/) (2024)
- [Knowledge-Augmented Reasoning Distillation for Small Language Models in Knowledge-Intensive Tasks](https://mlsanity.com/paper/2305.18395/) (2023)
- [TimeFilter: Patch-Specific Spatial-Temporal Graph Filtration for Time Series Forecasting](https://mlsanity.com/paper/2501.13041/) (2025)
- [LightTS: Lightweight Time Series Classification with Adaptive Ensemble Distillation -- Extended Version](https://mlsanity.com/paper/2302.12721/) (2023)
- [Large Language Model Guided Knowledge Distillation for Time Series Anomaly Detection](https://mlsanity.com/paper/2401.15123/) (2024)
- [Efficient Large-Scale Traffic Forecasting with Transformers: A Spatial Data Management Perspective](https://mlsanity.com/paper/2412.09972/) (2024)
- [DIVERSIFY: A General Framework for Time Series Out-of-distribution Detection and Generalization](https://mlsanity.com/paper/2308.02282/) (2023)
- [Distilling Large Language Models for Text-Attributed Graph Learning](https://mlsanity.com/paper/2402.12022/) (2024)
- [LightTR: A Lightweight Framework for Federated Trajectory Recovery](https://mlsanity.com/paper/2405.03409/) (2024)

## Built on by (most cited first, 20 of 20)

- [DBLoss: Decomposition-based Loss Function for Time Series Forecasting](https://mlsanity.com/paper/2510.23672/) (2025)
- [Enhancing Time Series Forecasting through Selective Representation Spaces: A Patch Perspective](https://mlsanity.com/paper/2510.14510/) (2025)
- [BLAST: Balanced Sampling Time Series Corpus for Universal Forecasting Models](https://mlsanity.com/paper/2505.17871/) (2025)
- [Towards Cross-Modality Modeling for Time Series Analytics: A Survey in the LLM Era](https://mlsanity.com/paper/2505.02583/) (2025)
- [Distilling Time Series Foundation Models for Efficient Forecasting](https://mlsanity.com/paper/2601.12785/) (2026)
- [CC-Time: Cross-Model and Cross-Modality Time Series Forecasting](https://mlsanity.com/paper/2508.12235/) (2025)
- [Distill Skills into Weights, Not Prompts: Abstract Skills as Privileged Signals for On-Policy Self-Distillation](https://mlsanity.com/paper/2608.09826/) (2026)
- [Augur: Modeling Covariate Causal Associations in Time Series via Large Language Models](https://mlsanity.com/paper/2510.07858/) (2025)
- [LoFT-LLM: Low-Frequency Time-Series Forecasting with Large Language Models](https://mlsanity.com/paper/2512.20002/) (2025)
- [Post-Training in Time Series Foundation Models: A Unifying Framework](https://mlsanity.com/paper/2607.20002/) (2026)
- [SynEVO: A neuro-inspired spatiotemporal evolutional framework for cross-domain adaptation](https://mlsanity.com/paper/2505.16080/) (2025)
- [LLMs Meet Cross-Modal Time Series Analytics: Overview and Directions](https://mlsanity.com/paper/2507.10620/) (2025)
- [IndexNet: Timestamp and Variable-Aware Modeling for Time Series Forecasting](https://mlsanity.com/paper/2509.23813/) (2025)
- [MM-ISTS: Cooperating Irregularly Sampled Time Series Forecasting with Multimodal Vision-Text LLMs](https://mlsanity.com/paper/2603.05997/) (2026)
- [From Time Series Analysis to Question Answering: A Survey in the LLM Era](https://mlsanity.com/paper/2506.11512/) (2025)
- [Invariant Representation Learning for Source-Free Time Series Forecasting with LLM-Centric Proxy Denoising](https://mlsanity.com/paper/2510.05589/) (2025)
- [Federated Reasoning Distillation Framework with Model Learnability-Aware Data Allocation](https://mlsanity.com/paper/2602.18749/) (2026)
- [PeakFocus: Bridging Peak Localization and Intensity Regression via a Unified Multi-Scale Framework for Electricity Load Forecasting](https://mlsanity.com/paper/2605.21550/) (2026)
- [Beyond Tokenization: Direct Timestep Embedding and Contrastive Alignment for Time-Series Question Answering](https://mlsanity.com/paper/2606.18986/) (2026)
- [Which Histories Matter for Time Series Forecasting? Learning Predictive Relevance with Future Supervision](https://mlsanity.com/paper/2608.23221/) (2026)

## Abstract (arXiv)

Multivariate time series forecasting (MTSF) endeavors to predict future observations given historical data, playing a crucial role in time series data management systems. With advancements in large language models (LLMs), recent studies employ textual prompt tuning to infuse the knowledge of LLMs into MTSF. However, the deployment of LLMs often suffers from low efficiency during the inference phase. To address this problem, we introduce TimeKD, an efficient MTSF framework that leverages the calibrated language models and privileged knowledge distillation. TimeKD aims to generate high-quality future representations from the proposed cross-modality teacher model and cultivate an effective student model. The cross-modality teacher model adopts calibrated language models (CLMs) with ground truth prompts, motivated by the paradigm of Learning Under Privileged Information (LUPI). In addition, we design a subtractive cross attention (SCA) mechanism to refine these representations. To cultivate an effective student model, we propose an innovative privileged knowledge distillation (PKD) mechanism including correlation and feature distillation. PKD enables the student to replicate the teacher's behavior while minimizing their output discrepancy. Extensive experiments on real data offer insight into the effectiveness, efficiency, and scalability of the proposed TimeKD.