arXiv subjects

Margaux Br{é}g{è}re

Publications and source records attributed to Margaux Br{é}g{è}re.

2 recordsLinked to original sources

arXiv2026

Sliding-Window Signatures as Features for Time Series Forecasting

The evolution of a time series is often influenced not only by its past values but also by external covariates, giving rise to forecasting with exogenous variables. Nonlinear and delayed effects between covariates and the target series make this task particularly challenging. We propose a forecasting framework based on Ridge regression with sliding-window signature features, combining the computational efficiency of (semi-)parametric models with the flexibility of nonparametric approaches. These features capture complex dependencies between the target and the exogenous variables without relying on prior assumptions about the form of these relationships or the influence of past observations. We establish theoretical guarantees in the discrete-time setting, including universality of approximation and stationarity for the sliding-window transform. To ease implementation, we introduce a novel sequential algorithm that exploits window overlap for efficient signature updates. The method is evaluated on both synthetic and real electricity demand data. Results show that signature features effectively encode temporal and nonlinear dependencies, yielding accurate forecasts competitive with those based on expert knowledge and recent neural network approaches.

stat.ME↗

arXiv2026

Encoding Time Series Dynamics with Sliding-Window Signatures for Online Forecasting

Accurate forecasting often relies on both past target values and exogenous variables as inputs. In many applications, however, the time series of interest are non-stationary and the relationship between target and inputs evolves over time, requiring forecasters that adapt online. Moreover, inputs affect the target not only through their current values but also through their recent joint dynamics. We address these challenges in three steps. First, to encode the series dynamics, we rely on signatures of the input paths over sliding windows. Motivated by the universality of linear functionals of signatures, we fit a regularized linear regression on these features to capture nonlinear, path-dependent effects. Second, the simplicity of the linear model allows us to update it online as new data arrives, using a Kalman filter to track dynamic effects. Third, to capture dependencies at several time scales, we combine forecasters built on different window lengths through online aggregation. For French national electricity load forecasting, our method outperforms various state-of-the-art approaches. It also remains competitive across several benchmark datasets with exogenous variables.

math.ST↗