Nonstationary Time Series Prediction Based on Deep Echo State Network Tuned by Bayesian Optimization

Yu-Ting Bai, Wei Jia, Xue-Bo Jin (), Ting-Li Su, Jian-Lei Kong and Zhi-Gang Shi
Additional contact information
Yu-Ting Bai: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China
Wei Jia: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China
Xue-Bo Jin: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China
Ting-Li Su: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China
Jian-Lei Kong: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China
Zhi-Gang Shi: School of Artificial Intelligence, Beijing Technology and Business University, Beijing 100048, China

Mathematics, 2023, vol. 11, issue 6, 1-22

Abstract: The predictions from time series data can help us sense development trends and make scientific decisions in advance. The commonly used forecasting methods with backpropagation consume a lot of computational resources. The deep echo state network (DeepESN) is an advanced prediction method with a deep neural network structure and training algorithm without backpropagation. In this paper, a Bayesian optimization algorithm (BOA) is proposed to optimize DeepESN to address the problem of increasing parameter scale. Firstly, the DeepESN was studied and constructed as the basic prediction model for the time series data. Secondly, the BOA was reconstructed, based on the DeepESN, for optimal parameter searching. The algorithm is proposed within the framework of the DeepESN. Thirdly, an experiment was conducted to verify the DeepESN with a BOA within three datasets: simulation data generated from computer programs, a real humidity dataset collected from Beijing, and a power load dataset obtained from America. Compared with the models of BP (backpropagation), LSTM (long short-term memory), GRU (gated recurrent unit), and ESN (echo state network), DeepESN obtained optimal results, which were 0.0719, 18.6707, and 764.5281 using RMSE evaluation. While getting better accuracy, the BOA optimization time was only 323.4 s, 563.2 s, and 9854 s for the three datasets. It is more efficient than grid search and grey wolf optimizer.

Keywords: echo state network; time series prediction; deep learning; Bayesian optimization (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1503/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1503/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:6:p:1503-:d:1102009

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().