Analysis Of Chinese Stock Market Based On Network Of Statistical Correlation Among Stocks

Serving as the barometer of the current national economy, the circulated stock value that stock market holds takes up approximately 60% to 80% of the whole GDP of each country, which makes the stock market an indispensable part of the national economy. The stock market is also an important economical operation index, making it a primary research target in national economy-related fields. Researching on stock fluctuations is an effective way to study in what condition stock market is running. People can learn from the fluctuation the general trend of stock market in order to optimize their investment allocation. Furthermore, studies on this aspect can help the government formulate corresponding economic policy for proper micro-economic control. Therefore, researches on stock fluctuation are of great significance for national economy, regional development as well as individual life. However, nowadays, most research findings of domestic stock market cannot present the structural features of the stock market as a whole, due to a lack of systematic analysis, in that most of these researches only focus on individual price forecast and various empirical analysis. In this paper, we creatively transform a lot of algorithms into data analysis of stock market, which are originally used in computer science or bio-informatics. We try to model the network of stock market with correlation between stocks fluctuations, and then deliver some research on the model to reach some knowledge of Chinese stock structure. Meanwhile, during the research, according to the specialty of stocks data, this paper also perform a lot of improvement or modification on the original algorithms, to either improve the efficiency or reduce the requirement of computing capability, in order to make these algorithms suitable for the data of stocks.This paper focus on research related works, and its structure follows steps of: first, finding proper algorithms, then running tests to modify the algorithms fitting the data, and finally doing holistic research. Steps in details are as following:First, independence analysis of time series is needed, and it is also required by later steps. We compared three common algorithms (e.g. BDS analysis, R/S analysis, and DFA analysis), and finally choose the DFA analysis, which is sensitive with long-term dependence but tolerable with short-term dependence, to run the first step of data selecting.Following step is to build the correlation network. The way we choose to set up the network is using Pearson correlation coefficient and P-value to judge the existence of edge between stocks, and then using per-comparison error rate to control the threshold of multi-test.Then, algorithms need to be tested, so that we could improve or modify them to fit the stocks data. We use the theory and algorithms which are former decided, to perform several tests over samples, and then modify the algorithms suitable for data. After several steps of tests, the results show that all methods we choose before are ready for holistic usage.Finally, analysis over holistic networks of Chinese stock market is performed. We perform analysis step by step: first on simple visible analysis, then motif analysis, and finally fuzzy clustering analysis to dig information hidden behind the fluctuation of stocks.After these researches, we get some conclusions as following: the topology of network over Chinese stock market becomes more and more diffusing, and the correlations among stocks become weaker as well, which means stock fluctuations are becoming independent; besides, in our correlation networks, we find that the frequency of motifs with no more than 5 nodes seem no difference between stock networks and random networks which have the same degree-distribution as former one, but the Z-score of motifs with more than 5 nodes is apparently high, which shows these motifs are functional to some extent; and after overall fuzzy clustering analysis, we find with a standardλ value over years, the number of clusters become more and more, the coefficient of cluster also implies this trend will continue. All above shows that, to some extent, Chinese stock market is stepping into a model of weak-efficient market, which is proved more mature and effective; besides, the motifs and cluster we find are also available for other research such as portfolio analysis.