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.

The air pollution caused by particulate matter (PM) has become a public health issue due to the risks to human life and the environment. The PM concentration in the air causes haze and affects the lungs and the heart, leading to reduced visibility, allergic reactions, pneumonia, asthma, cardiopulmonary diseases, lung cancer, and even death. In this context, the development of systems for monitoring, forecasting, and controlling emissions plays an important role. The literature about forecasting systems based on Artificial Neural Networks (ANNs) ensembles has been highlighted regarding statistical accuracy and efficiency. In this article, trainable and non-trainable combination methods are used for PM10 and PM2.5 (particles with an aerodynamic diameter less than 10 and 2.5 micrometers, respectively) time series forecasting for eight different locations, in Finland and Brazil, for different periods. Trainable ensembles based on ANNs, linear regression, and Copulas are compared with non-trainable combinations (mean and median), single ANNs, and linear statistical approaches. Different models are considered so far, including Autoregressive model (AR), Autoregressive and Moving Average Model (ARMA), Infinite Impulse Response Filters (IIR), Multilayer Perceptron (MLP), Radial Basis Function Networks (RBF), Extreme Learning Machines (ELM), Echo State Networks (ESN), and Adaptive Network Fuzzy Inference System (ANFIS). The use of ANNs ensembles, mainly combined with MLP, leads to a better one step ahead forecasting performance. The use of robust air pollution forecasting tools is prime to assist governments in managing air pollution issues like hospital collapse during adverse air quality situations. In this sense, our study is indirectly related to the following United Nations sustainable development goals: SDG 3 - good health and well-being and SDG 11 - sustainable cities and communities.