Detrended partial cross-correlation analysis-random matrix theory for denoising network construction

A denoised complex network framework employing a detrended partial cross-correlation analysis-based coefficient for achieving the intrinsic scale-dependent correlations between each pair of variables is developed to explore the interrelatedness of multiple nonstationary variables in the real-world. In doing this, we start with introducing the detrended partial cross-correlation coefficient into random matrix theory, and executing a denoising process through correlation matrix reconfiguration, which is followed by utilizing the denoised correlation matrix to construct a planar maximally filtered graph network. It allows us assess the interactions among complex objects more accurately. The effectiveness of our proposed method is validated through the numerical experiments simulating the eigenvalue distribution, and the results show that our method accurately locates the maximum eigenvalue at a specific scale, but existing methods fail to achieve. As a practical application, we also apply the proposed denoising network framework to investigate the co-movement behavior of PM2.5\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$_{2.5}$$\end{document} air pollution of North China and the linkage of commodity futures prices in China. The results show that the denoising process significantly enhances the information content of the network, revealing several interesting insights regarding network properties.