Network Entropies of the Chinese Financial Market

Abstract

Based on the data from the Chinese financial market, this paper focuses on analyzing three types of network entropies of the financial market, namely, Shannon, Renyi and Tsallis entropies. The findings suggest that Shannon entropy can reflect the volatility of the financial market, that Renyi and Tsallis entropies also have this function when their parameter has a positive value, and that Renyi and Tsallis entropies can reflect the extreme case of the financial market when their parameter has a negative value.

Stock Net Entropy: Evidence from the Chinese Growth Enterprise Market

“…The other one called network structure entropy, focuses on the network structure, including node degree sequences, edge weights, clustering coefficients or others to demonstrate the heterogeneity of the network structure. These include Wu structure entropy defined with node difference [ 33 ], Shannon entropy, Renyi entropy, and Tsallis entropy defined with edge weight [ 53 ], and Shannon entropy defined with node degree, clustering coefficients, or centrality [ 54 ].…”

“…Although various entropies have been adopted to study financial markets [ 37 , 38 , 39 , 40 , 41 ], there are limited papers analyzing financial market heterogeneity with network entropy. Among the rare examples are Li et al [ 53 ] who considered three types of network entropies to analyze the financial market. Nie and Song [ 55 ] introduced a standardized Rényi entropy to capture the structural differences of financial correlation-based networks.…”

Entropies of the Chinese Land Use/Cover Change from 1990 to 2010 at a County Level

“…In short, it is reasonable to analyze the changes in regional landuse structures using Shannon entropy. [30]. The type of Country ID is as in Figure 2. …”

“…Tsallis entropy and Renyi entropy are the generalized forms with an adjustment parameter [30]; it is a new information measuring method of statistical physics, which can provide satisfactory physical interpretations for a mixed system. The definition is as follows:…”

“…However, there is limited research on the entropy of LUCC. Rare instances adopt a Shannon entropy-related measurement [30] to quantify the robustness of the evolving LUCC, and propose a statistical visualization model to quantify the Chinese LUCC space-time structure at different scales. The volatility and extreme case of the LUCC are needed to quantify the evolving of Chinese LUCC organization.…”