Résumé
Accurate forecasting of macroeconomic and energy-related time series remains challenging due to structural instability, strong cross-dependencies, and pronounced deviationsfrom linear Gaussian assumptions. While VARIMA models offer a transparent multivariate framework, their empirical performance is often limited in environments characterizedby volatility clustering and nonlinear adjustment dynamics. Conversely, machine learning methods provide greater flexibility but may suffer from instability and limited interpretability in multivariate economic settings. This paper proposes a hybrid multivariateforecasting framework that combines VARIMA models with machine learning algorithmsin a residual-based architecture. VARIMA is used as a disciplined linear filter to capturecommon dynamics across macroeconomic, financial, and energy variables, while machinelearning models learn nonlinear corrections from the multivariate residuals. The approachis evaluated using monthly data spanning January 1999 to August 2025, including multiple crisis episodes and a turbulent out-of-sample period. Extensive diagnostic tests revealsystematic violations of linear model assumptions, motivating hybridization. Forecastingresults show that hybrid VARIMA–machine learning models consistently outperform bothstandalone VARIMA and pure machine learning specifications in terms of accuracy androbustness. The findings demonstrate that residual-based hybridization provides an interpretable and effective strategy for integrating machine learning into multivariate economicforecasting.