Multi-step Time Series Forecasting Using Ridge Polynomial Neural Network with Error-Output Feedbacks

  • Waddah WaheebEmail author
  • Rozaida Ghazali
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 652)


Time series forecasting gets much attention due to its impact on many practical applications. Higher-order neural network with recurrent feedback is a powerful technique which used successfully for forecasting. It maintains fast learning and the ability to learn the dynamics of the series over time. For that, in this paper, we propose a novel model, called Ridge Polynomial Neural Network with Error-Output Feedbacks (RPNN-EOF), which combines three powerful properties: higher order terms, output feedback and error feedback. The well-known Mackey–Glass time series is used to evaluate the forecasting capability of RPNN-EOF. Results show that the proposed RPNN-EOF provides better understanding for the Mackey–Glass time series with root mean square error equal to 0.00416. This error is smaller than other models in the literature. Therefore, we can conclude that the RPNN-EOF can be applied successfully for time series forecasting. Furthermore, the error-output feedbacks can be investigated and applied with different neural network models.


Time series forecasting Ridge polynomial neural network with error-output feedbacks Higher order neural networks Recurrent neural networks Mackey–glass equation 



The authors would like to thank Universiti Tun Hussein Onn Malaysia (UTHM) and Ministry of Higher Education (MOHE) Malaysia for financially supporting this research under the Fundamental Research Grant Scheme (FRGS), Vote No. 1235.


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© Springer Nature Singapore Pte Ltd. 2016

Authors and Affiliations

  1. 1.Faculty of Computer Science and Information TechnologyUniversiti Tun Hussein Onn MalaysiaParit RajaMalaysia
  2. 2.Computer Science DepartmentHodeidah UniversityHodeidahYemen

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