Title: Time Series Forecasting: Empowering Exogenous Data with Shape Morphing
Primary area: learning on time series and dynamical systems
Keywords: Temporal Saliency Detection, Exogenous Data, Time Series, Forecasting, Transformer Models, Multivariate, Morphing

Abstract: Time series forecasting often relies on patterns extracted from historical target dynamics, yet exogenous variables can provide valuable additional signal. Importantly, such variables are typically informative only in specific intervals and irrelevant elsewhere. We refer to this phenomenon as temporal saliency of exogenous variables, i.e., the time-varying relevance of external inputs for predicting the target series. In this paper, we tackle the "forecasting with exogenous variables" problem, where the model receives multiple input channels but predicts only one target variable. Recent studies have shown that channel-dependent Transformer architectures might be outperformed by simple channel-independent linear models, suggesting that current cross-attention mechanisms suffer to fully profit from exogenous information. To address this, we propose a morphing framework that adaptively reshapes exogenous time series before forecasting. For each channel and time step, a morphing function computes a ratio from the local relationship between the exogenous input and the target series and amplifies useful intervals accordingly. We instantiate morphing functions with interpretable information-theoretic metrics such as correlation, covariance, entropy, and mutual information, and evaluate them in ablation studies for long-horizon forecasting and state-of-the-art Transformer-based architectures. Results show that morphing is capable to yield significant improvements in certain dataset–model combinations. These findings highlight morphing as a simple yet effective way to enhance the utility of exogenous information and close part of the performance gap between linear and Transformer-based forecasting methods.

TL;DR: The paper presents results of an extensive time series forecasting ablation test, with exogenous data on multiple transformer model, which reveal strong indications that shape morphing of exogenous data positively affect forecasting accuracy.