Towards history-aware sensitivity analysis for time series

¹ CMAP, CNRS, École polytechnique, Institut Polytechnique de Paris, 91120 Palaiseau, France
² COSYS, Université Gustave Eiffel, 14-20 Boulevard Newton, 77447 Marne-la-Vallée, France

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 12 September 2025
Accepted: 28 April 2026

Abstract

Explaining the outcome of dynamical systems is non-trivial due to the temporal nature and correlation of the variables. In this work, we propose a novel framework of history-aware sensitivity analysis for stationary time-series to quantify different memory effects and clarify their roles. For this purpose, we decompose the output time series into non-correlated components, namely the instantaneous component and the memory components. The latter are sorted in decreasing order of variance to reflect the importance of the variables. We highlight the compensation phenomena between the resulting components and illustrate them in the case of independent variables in a linear setting. To enable history-aware explanations, variance-based sensitivity indices are derived from the obtained decomposition. We demonstrate the effectiveness of our methodology in providing insights to explain output time-series in both synthetic and real-world cases.