Dynamic structure of stock communities: A comparative study between stock returns and turnover rates

The detection of community structure in stock market is of theoretical and practical significance for the study of financial dynamics and portfolio risk estimation. We here study the community structures in Chinese stock markets from the aspects of both price returns and turnover rates, by using a combination of the PMFG and infomap methods based on a distance matrix. We find that a few of the largest communities are composed of certain specific industry or conceptional sectors and the correlation inside a sector is generally larger than the correlation between different sectors. In comparison with returns, the community structure for turnover rates is more complex and the sector effect is relatively weaker. The financial dynamics is further studied by analyzing the community structures over five sub-periods. Sectors like banks, real estate, health care and New Shanghai take turns to compose a few of the largest communities for both returns and turnover rates in different sub-periods. Several specific sectors appear in the communities with different rank orders for the two time series even in the same sub-period. A comparison between the evolution of prices and turnover rates of stocks from these sectors is conducted to better understand their differences. We find that stock prices only had large changes around some important events while turnover rates surged after each of these events relevant to specific sectors, which may offer a possible explanation for the complexity of stock communities for turnover rates

Signature-Based Community Detection for Time Series

Community detection for time series without prior knowledge poses an open challenge within complex networks theory. Traditional approaches begin by assessing time series correlations and maximizing modularity under diverse null models. These methods suffer from assuming temporal stationarity and are influenced by the granularity of observation intervals. In this study, we propose an approach based on the signature matrix, a concept from path theory for studying stochastic processes. By employing a signature-derived similarity measure, our method overcomes drawbacks of traditional correlation-based techniques. Through a series of numerical experiments, we demonstrate that our method consistently yields higher modularity compared to baseline models, when tested on the Standard and Poor's 500 dataset. Moreover, our approach showcases enhanced stability in modularity when the length of the underlying time series is manipulated. This research contributes to the field of community detection by introducing a signature-based similarity measure, offering an alternative to conventional correlation matrices

Pearson coefficient matrix for studying the correlation of community detection scores in multi-objective evolutionary algorithm

Assessing a community detection algorithm is a difficult task due to the absence of finding a standard definition for objective functions to accurately identify the structure of communities in complex networks. Traditional methods generally consider the detecting of community structure as a single objective issue while its optimization generally leads to restrict the solution to a specific property in the community structure. In the last decade, new community detection models have been developed. These are based on multi-objective formulation for the problem, while ensuring that more than one objective (normally two) can be simultaneously optimized to generate a set of non-dominated solutions. However the issue of which objectives should be co-optimized to enhance the efficiency of the algorithm is still an open area of research. In this paper, first we generate a candidate set of partitions by saving the last population that has been generated using single objective evolutionary algorithm (SOEA) and random partitions based on the true partition for a given complex network. We investigate the features of the structure of communities which found by fifteen existing objectives that have been used in literature for discovering communities. Then, we found the correlation between any two objectives using the pearson coefficient matrix. Extensive experiments on four real networks show that some objective functions have a strong correlation and others either neutral or weak correlations