Hybrid systems, which combine statistical and machine learning (ML) techniques using residual (error forecasting) modeling, have been highlighted in the literature due to their accuracy and ability to forecast time series with different characteristics. In these architectures, a crucial task is the proper modeling of the residuals since they may present random fluctuations, complex nonlinear patterns, and heteroscedastic behavior. Hence, the selection, specification, and training of one ML model to forecast the residuals are costly and challenging tasks since issues, such as underfitting, overfitting, and misspecification, can lead to a system with low accuracy or even deteriorate the linear forecast of the time series. This article proposes a hybrid system, named dynamic residual forecasting (DReF), that employs a modified dynamic selection (DS) algorithm to decide: the most suitable ML model to forecast a pattern of the residual series and if it is a promising candidate to increase the accuracy of the time series forecast from the linear combination. Thus, the DReF aims to reduce the uncertainty of the ML model selection and avoid the deterioration of the time series forecast. Furthermore, the proposed system searches for the most suitable parameters of the DS algorithm for each data set. In this article, the proposed method uses a pool of five ML models widely adopted in the literature: multilayer perceptron, support vector regression, radial basis function, long short-term memory, and convolutional neural network. An experimental evaluation was conducted using ten well-known time series. The results show that the DReF obtains superior results for the majority of the data sets compared with single and hybrid models of the literature.