# Forecasting Multivariate Time Series under Predictive Heterogeneity: A Validation-Driven Clustering Framework

arXiv: https://arxiv.org/abs/2604.13748 · HTML: https://mlsanity.com/paper/2604.13748/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 8 of its 30 references that are in the map.
- First posted on arXiv 15 Apr 2026.

## Builds on (most cited first, 8 of 8)

- [Empirical Evaluation of Gated Recurrent Neural Networks on Sequence Modeling](https://mlsanity.com/paper/1412.3555/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Principles and Algorithms for Forecasting Groups of Time Series: Locality and Globality](https://mlsanity.com/paper/2008.00444/) (2020)
- [FCPCA: Fuzzy clustering of high-dimensional time series based on common principal component analysis](https://mlsanity.com/paper/2505.07276/) (2025)
- [An Empirical Experiment on Deep Learning Models for Predicting Traffic Data](https://mlsanity.com/paper/2105.05504/) (2021)
- [Time series clustering based on prediction accuracy of global forecasting models](https://mlsanity.com/paper/2305.00473/) (2023)
- [A Gentle Introduction to Conformal Time Series Forecasting](https://mlsanity.com/paper/2511.13608/) (2025)
- [Robust fuzzy clustering for high-dimensional multivariate time series with outlier detection](https://mlsanity.com/paper/2510.26982/) (2025)

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

- [Adaptive Multi-Scale Forecasting and Gate-Localized Conformal Prediction for Multivariate Nonstationary Time Series](https://mlsanity.com/paper/2607.23165/) (2026)

## Abstract (arXiv)

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series based on representation similarity, we define partitions through out-of-sample predictive performance, thereby aligning data organization with predictive risk, defined as expected out-of-sample loss and approximated via validation error. Cluster assignments are iteratively updated using validation losses for both point (Huber) and probabilistic (pinball) forecasting, improving robustness to heavy-tailed errors and local anomalies. To ensure reliability, we introduce a leakage-free fallback mechanism that reverts to a global model whenever specialization fails to improve validation performance, providing a safeguard against performance degradation under a strict training-validation-test protocol. Experiments on large-scale traffic datasets demonstrate consistent improvements over strong baselines while avoiding degradation when heterogeneity is weak. Overall, the proposed framework provides a principled and practically reliable approach to adaptive pooling in high-dimensional forecasting problems.