We propose a flexible rolling window estimation procedure which improves forecasting accuracy of misspecified linear autoregressive models. The method assigns different weights to data points in the observed sample which can be useful in the presence of data generating processes featuring structural breaks, complex nonlinearities, or other time-varying properties which cannot be easily captured by model design. We show how the window can be regularized by means of cross-validation. In a set of Monte Carlo experiments we reveal that the estimation method can significantly improve the forecasting accuracy of autoregressive models. In an empirical study, we achieve higher forecasting accuracy for U.S. Industrial Production during the great recession by giving more weight to observations from past recessions. Similar findings are found for other macroeconomic time series and for the 2008-2009 global financial crisis and the COVID-19 recession in 2020.