Adaptive Multi-Scale Forecasting and Gate-Localized Conformal Prediction for Multivariate Nonstationary Time Series

2026-07-25

AI Summary

This work addresses the challenge of accurate point forecasting and reliable uncertainty quantification for non-stationary multivariate time series by proposing the ABF-T-GLCP framework. The method enhances point prediction accuracy through adaptive learning of predictive state representations, integrating a multi-scale temporal expert gating mechanism with sparse cross-series predictive transfer. It further introduces gated local conformal prediction (GLCP)—a novel approach that uniquely combines gated states with temporal proximity to enable model-agnostic, locally calibrated conformal prediction. This core innovation facilitates joint adaptation of point forecasts and prediction intervals in dynamic environments while guaranteeing local coverage validity. Experiments demonstrate that the proposed method significantly outperforms existing approaches on high-frequency commodity forecasting benchmarks, yielding substantially narrower prediction intervals with empirical coverage closely matching nominal levels, and exhibits strong generalization performance in out-of-domain financial scenarios.

Abstract

We propose ABF-T-GLCP, a model-agnostic framework for forecasting and uncertainty quantification in nonstationary multivariate time series. The central idea is to learn an adaptive predictive state representation for point forecasting and reuse it for conformal calibration. The forecasting module combines horizon-specific temporal experts through a learned gate and refines predictions using sparse predictive transfer across related series. The uncertainty module, Gate-Localized Conformal Prediction (GLCP), uses the learned gate state, together with temporal recency, to select locally relevant calibration residuals, thereby coupling uncertainty calibration to the predictive regimes used by the forecasting model. This shared representation allows point forecasts and prediction intervals to adapt consistently under evolving temporal dynamics while retaining the model-agnostic nature of conformal prediction and yielding approximate local coverage under mild stability conditions. Experiments on a large-scale high-frequency commodity forecasting benchmark show consistent gains in point forecasting accuracy and substantially narrower prediction intervals with empirical coverage close to the nominal level. Additional results indicate that the framework extends beyond the motivating financial application.

Problem

• nonstationary time series
• multivariate forecasting
• uncertainty quantification
• conformal prediction
• adaptive forecasting

Innovation

• adaptive forecasting
• conformal prediction
• nonstationary time series
• gate-localized calibration
• multivariate time series