ORIGINAL RESEARCH article
Front. Phys.
Sec. Statistical and Computational Physics
Features of Chinese Copper Future Return: Based on A Markov Network Approach
Provisionally accepted
Hongkun Zhao1
Qishen Chen1*
Yanfei Zhang1
Kun Wang1
Liuguo Shao2
Chenghong Shang1
Hua Zhang2Ye Zhang1Dan Song3- 1Institute of Mineral Resources, Chinese Academy of Geological Sciences, Beijing, China
- 2School of Business, Central South University, Changsha, China, Changsha, China
- 3China University of Geosciences Beijing, Beijing, China
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Introduction: Copper has the dual attributes of industrial raw materials and financial assets, and its price formation mechanism presents complex non-linear characteristics under the dual role of supply and demand mechanism and financialization. The structural upgrading of industrial demand and the risk contagion effect in the futures market make it difficult to effectively analyze the fluctuation characteristics of copper price in the traditional linear analytical framework. Consequently, it is significant to explore the fluctuation characteristics of copper futures price from the perspective of complex system science. Methods: This study employed complex network theory and the Markov switching model to develop a Markov network model of copper futures and to explore the evolving characteristics of copper prices. Results and discussion: This study finds that: (1) There are 243 price switch states in theory, but only 126 types of states actually occur. Among them, 33 high-frequency states account for 90% of the total number of times, indicating that price fluctuations are active and concentrated in a regular manner. (2) The average path length of network state transition is 5.4, and the symmetry coefficient is 0.99, which shows that the transition efficiency is high but the path is highly asymmetric. (3) There are some nodes with low degree centrality and high betweenness centrality in the network, which act as mediators in the network, connecting the transitions between states. (4) The network has a significant association structure, and we find that the state nodes have a relatively obvious "rich club" effect. This study reveals that the nonlinear dynamics and network structures of copper future return.
Keywords: Copper, Future return, Markov network, Leiden's algorithm, Vincent's algorithm
Received: 25 Sep 2025; Accepted: 20 Nov 2025.
Copyright: © 2025 Zhao, Chen, Zhang, Wang, Shao, Shang, Zhang, Zhang and Song. This is an open-access article distributed under the terms of the Creative Commons Attribution License (CC BY). The use, distribution or reproduction in other forums is permitted, provided the original author(s) or licensor are credited and that the original publication in this journal is cited, in accordance with accepted academic practice. No use, distribution or reproduction is permitted which does not comply with these terms.
* Correspondence: Qishen Chen, chenqishen@126.com
Disclaimer: All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article or claim that may be made by its manufacturer is not guaranteed or endorsed by the publisher.