Defining and applying prediction performance metrics on a recurrent NARX time series model

Nonlinear autoregressive moving average with exogenous inputs (NARMAX) models have been successfully demonstrated for modeling the input–output behavior of many complex systems. This paper deals with the proposition of a scheme to provide time series prediction. The approach is based on a recurrent NARX model obtained by linear combination of a recurrent neural network (RNN) output and the real data output. Some prediction metrics are also proposed to assess the quality of predictions. This metrics enable to compare different prediction schemes and provide an objective way to measure how changes in training or prediction model (neural network architecture) affect the quality of predictions. Results show that the proposed NARX approach consistently outperforms the prediction obtained by the RNN neural network.