Nonlinear time series forecasting with Bayesian neural networks

•Evolutionary Monte Carlo algorithm is proposed to train Bayesian neural networks.•The proposed approach is based on Gaussian approximation of Bayesian learning.•Monte Carlo methods is integrated with GA and fuzzy membership functions.•Time series forecasting was made over the weekly sales of a Finance Magazine.•All the methods were compared in terms of forecasting performance on the test data.

The Bayesian learning provides a natural way to model the nonlinear structure as the artificial neural networks due to their capability to cope with the model complexity. In this paper, an evolutionary Monte Carlo (MC) algorithm is proposed to train the Bayesian neural networks (BNNs) for the time series forecasting. This approach called as Genetic MC is based on Gaussian approximation with recursive hyperparameter. Genetic MC integrates MC simulations with the genetic algorithms and the fuzzy membership functions. In the implementations, Genetic MC is compared with the traditional neural networks and time series techniques in terms of their forecasting performances over the weekly sales of a Finance Magazine.