Are neural networks able to forecast nonlinear time series with moving average components?

In nonlinear time series forecasting, neural networks are interpreted as a nonlinear autoregressive models because they take as inputs the previous values of the time series. However, the use of neural networks to forecast nonlinear time series with moving components is an issue usually omitted in the literature. In this article, we investigate the use of traditional neural networks for forecasting nonlinear time series with moving average components and we demonstrate the necessity of formulating new neural networks to adequately forecast this class of time series. Experimentally we show that traditional neural networks are not able to capture all the behavior of nonlinear time series with moving average components, which leads them to have a low capacity of forecast.