Predicting regional carbon price in China based on multi-factor HKELM by combining secondary decomposition and ensemble learning

PLOS ONE RESEARCH ARTICLE Predicting regional carbon price in China based on multi-factor HKELM by combining secondary decomposition and ensemble learning Beibei Hu ID, Yunhe Cheng* School of Economics and Management, Anhui University of Science and Technology, Huainan, China a1111111111 a1111111111 a1111111111 a1111111111 a1111111111 OPEN ACCESS Citation: Hu B, Cheng Y (2023) Predicting regional carbon price in China based on multi-factor HKELM by combining secondary decomposition and ensemble learning. PLoS ONE 18(12): e0285311. https://doi.org/10.1371/journal.pone.0285311 Editor: Nebojsa Bacanin, Univerzitet Singidunum, SERBIA Received: February 8, 2023 Accepted: April 19, 2023 Published: December 12, 2023 Copyright: © 2023 Hu, Cheng. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited. Data Availability Statement: The data are available on Dryad; DOI: https://doi.org/10.5061/dryad. qnk98sfms. (A) The data of Guangzhou’s carbon price was collected from the Guangzhou Carbon Emission Exchange website(http://www. cnemission.cn). (B) The data of Hubei’s carbon price is collected from China Hubei Emission Exchange (https://www.hbets.cn/list/13.html). (C) The Shanghai securities composite index collected from investing (https://cn.investing.com/). (D) The daily mean temperature in Guangzhou and Hubei Wuhan is from NOAA (https://www.ncei.noaa.gov/ data/global-summary-of-the-day/archive/). (E) The * Abstract Accurately predicting carbon price is crucial for risk avoidance in the carbon financial market. In light of the complex characteristics of the regional carbon price in China, this paper proposes a model to forecast carbon price based on the multi-factor hybrid kernel-based extreme learning machine (HKELM) by combining secondary decomposition and ensemble learning. Variational mode decomposition (VMD) is first used to decompose the carbon price into several modes, and range entropy is then used to reconstruct these modes. The multi-factor HKELM optimized by the sparrow search algorithm is used to forecast the reconstructed subsequences, where the main external factors innovatively selected by maximum information coefficient and historical time-series data on carbon prices are both considered as input variables to the forecasting model. Following this, the improved complete ensemble-based empirical mode decomposition with adaptive noise and range entropy are respectively used to decompose and reconstruct the residual term generated by VMD. Finally, the nonlinear ensemble learning method is introduced to determine the predictions of residual term and final carbon price. In the empirical analysis of Guangzhou market, the root mean square error(RMSE), mean absolute error (MAE) and mean absolute percentage error (MAPE) of the model are 0.1716, 0.1218 and 0.0026, respectively. The proposed model outperforms other comparative models in predicting accuracy. The work here extends the research on forecasting theory and methods of predicting the carbon price. 1 Introduction The warming climate threatens human health and sustainable development. It is mainly due to the increasing of carbon dioxide (CO2) concentration in the atmosphere. According to the report released by the national oceanic and atmospheric administration of the United States in 2022, the global average concentration of CO2 in the atmosphere was 421 ppm, nearly 50% higher than the concentration of 280 ppm before industrialization. Based on the statistical review of world energy released in 2022, the CO2 emissions of China accounted for 30.89% of the global total, making it the largest emitter of the CO2 [1]. Therefore, it is urgent for China to PLOS ONE | https://doi.org/10.1371/journal.pone.0285311 December 12, 2023 1 / 24 PLOS ONE rest are from the WIND database (http://www. wind.com.cn/). Funding: This research was funded by the major project of the National Social Science Foundation of China, the grant number is 22ZDA112. The funders had no role in study design, data collection and analysis, decision to publish, or preparation of the manuscript. Competing interests: The authors have declared that no competing interests exist. Predicting regional carbon price in China based on multi-factor HKELM reduce CO2 emissions. In order to promote carbon emissions reduction, China has formed the "7+2" development pattern of regional carbon markets. Specifically, it has established seven pilot carbon markets and two non-pilot carbon markets [2]. Moreover, regional carbon markets are conducive to promoting the growth of low-carbon industries as well as energy transformation. China’s national carbon market commenced online trading in July 2021. The carbon market is important for China to realize its aims at achieving the carbon peak and carbon neutralization. It is noteworthy that the national market is immature in market operation and system design, which requires regional carbon emissions trading markets to accumulate operational experience [3]. Carbon market price is one of the core indicators of the carbon market. According to the Kyoto Protocol, the carbon emission quotas traded in financial markets have commodity-related as well as financial attributes [4]. Its price can indicate the cost of carbon emission abatement for the economy [5]. It can compel enterprises to optimize their resource allocation to achieve their emissions reduction targets at the lowest cost [6]. However, in the complex global economic environment, China’s carbon market price fluctuates sharply and transaction risks increase. The drastic fluctuation of the carbon market price is too high or too low, which is not conducive to the long-term stable operation of the carbon market. Reasonable carbon emission quota pricing is an effective means of reducing greenhouse gas emissions [7], which will provide an effective price incentive signal for emission reduction enterprises. Consequently, accurate predicting of carbon price can provide valuable information for market participants to manage associated risks resulted from changes in price and for policy-makers to formulate relevant policies. Carbon prices exhibit nonlinear and nonstationary characteristics due to various factors [8]. It makes them challenging to predict. The aim of this research is to develop a combined framework for forecasting the regional carbon prices. The main contributions of this article can be illustrated as follows: (1) The multi-factor HKELM model is introduced to forecast carbon price. External factors influencing the carbon price and historical data on it are taken as input of the HKELM model to make the expression capability of the forecasting model of China’s regional carbon price closer to reality. (2) Ensemble learning based on the SSA-HKELM is introduced to integrate the results (...truncated)