Ridge Polynomial Neural Network with Error Feedback for Recursive Multi-step Forecast Strategy: A Case Study of Carbon Dioxide Emissions Forecasting

Abstract

Neural networks (NNs) have been used extensively for forecasting problems. NN with error feedbacks is a type of NNs that showed more accurate forecasts compared to feedforward NNs and NNs with output feedbacks with some forecasting problems. The main issue with NN s with error feedbacks appears when there is a need for recursive multi-step forecast strategy because the observed values must be known in order to calculate network errors. This paper proposes to use the last calculated error after finishing training NNs with error feedbacks because the observed values are unknown. This last calculated error is used as a fixed value when producing forecasts using recursive multi-step forecast strategy. For that, this paper investigated this simple solution with a NN with error feedback called the ridge polynomial neural network with error feedback (RPNN-EF). Carbon dioxide emissions for three countries in the organization of the petroleum exporting countries (OPEC) were used in this investigation. The forecasting accuracy of RPNN-EF was compared with seven forecasting methods. According to the obtained results, on average, the proposed solution produces reasonable forecasts compared to the seven forecasting methods. Therefore, this solution can be suggested for NNs with error feedbacks for recursive multi-step forecast strategy.