Structural vector autoregressions are used to compute impulse response functions (IRF) for persistent data. Existing multiple-parameter inference requires cumbersome pretesting for unit roots, cointegration, and trends with subsequent stationarization. To avoid pretesting, we propose a novel \emph{dependent wild bootstrap} procedure for simultaneous inference on IRF using local projections (LP) estimated in levels in possibly \emph{nonstationary} and \emph{heteroscedastic} SVARs. The bootstrap also allows efficient smoothing of LP estimates. We study IRF to US monetary policy identified using FOMC meetings count as an instrument for heteroscedasticity of monetary shocks. We validate our method using DSGE model simulations and alternative SVAR methods.