Recursive linear models optimized by bioinspired metaheuristics to streamflow time series prediction

Abstract Time series forecasting problems are often addressed using linear techniques, especially the autoregressive (AR) models, due to their simplicity combined with good performances. It is possible to generalize a linear predictor by allowing infinite impulse response (IIR) through the addition of feedback loops, as occurs in the autoregressive and moving average (ARMA) models and IIR filters. However, the calculation of the free coefficients of these structures is more complex, as the optimization problem has no closed‐form solution. This work conducts an extensive investigation on the use of linear models to predict monthly seasonal streamflow series associated with Brazilian hydroelectric plants. The main goal is to reach the best achievable performance with linear approaches. We propose the application of recursive models, estimating their parameters with the aid of bioinspired metaheuristics: particle swarm optimization (PSO), genetic algorithm (GA), differential evolution (DE), and two immune‐inspired algorithms, the CLONALG, and the artificial immune network for optimization (Opt‐aiNet). The AR model is also considered. The results to multistep ahead forecasting indicated that the insertion of feedback loops increased the performances, with ARMA being the best predictor. The DE, PSO, and GA led to the minimum values of mean‐squared error during the tests, while DE yielded the smallest dispersion.