Nonlinear combination method of forecasters applied to PM time series

Hybrid systems that combine Artificial Neural Networks with other forecasters have been widely employed for time series forecasting. In this context, some architectures use temporal patterns extracted from the error series (residuals), i.e., the difference between the time series and the forecasting of this time series. These architectures have reached relevant theoretical and practical results. However, in the learning process of complex time series using these hybrid systems two open questions arise: it is hard to ensure that the linear and nonlinear patterns, underlying the time series, are properly modeled; and the best function to combine the time series forecaster and error series forecaster is unknown. In this context, this work proposes a Nonlinear Combination (NoLiC) method to combine forecasters. The NoLiC method is a hybrid system that is composed of two steps: i) estimation of the models' parameters for the time series and their respective residuals, and ii) search for the best function that combines these models using a multi-layer perceptron. Experimental simulations are conducted using four real-world complex time series of great importance for public health and evaluated using six performance measures. The results show that the NoLiC method reaches superior results when compared with literature works.