SummaryIn this paper we introduce a nonparametric estimation method for a large Vector Autoregression (VAR) with time‐varying parameters. The estimators and their asymptotic distributions are available in closed form. This makes the method computationally efficient and capable of handling information sets as large as those typically handled by factor models and Factor Augmented VARs. When applied to the problem of forecasting key macroeconomic variables, the method outperforms constant parameter benchmarks and compares well with large (parametric) Bayesian VARs with time‐varying parameters. The tool can also be used for structural analysis. As an example, we study the time‐varying effects of oil price shocks on sectoral U.S. industrial output. According to our results, the increased role of global demand in shaping oil price fluctuations largely explains the diminished recessionary effects of global energy price increases.