Network-based Stock Market Model And Series Analysis

For more than ten years we have witnessed an avalanche of investigation ofcomplex networks, including theoretical approaches and application in diverseresearch fields such as economics, sociology, biology, economic-physics. It has been aan important branch of statistical physics. In this thesis, from viewpoint of complexnetwork we develop several to analyze stock markets and the tools are used to analyzeShanghai Stock market as a typical example.Firstly, we propose a new method, double-factor visibility graph(DVG), thatallow us to transform two time series into a complex network. For fractionalBrownian motions (fBm) and empirical financial series in Shanghai Stock Market,degree distributions obey power-law. Scaling exponent mainly depends on the serieswith smaller value of Hurst index.Secondly, Ising model is used to simulate interactions between networked tradersin stock market. Relationship network between traders is then constructed fromcorrelation coefficient matrix of behaviors of traders. In this so-called functionalnetwork, nodes have older ages in structural network tend to have greater degrees andbetweenness. They are more likely to reach consensus with others. We detect also theK-cores of function network, which may be useful in controlling on networks.Finally, a concept called balanced estimator of diffusion entropy is proposed todetect quantitatively scaling in short time series. The effectiveness is verified bydetecting successfully scaling properties for a large number of artificial fractionalBrownian motions. It is also used to detect scaling in the Shanghai Stock Index, fivestock catalogs, and a total of134stocks collected from the Shanghai Stock ExchangeMarket. The scaling exponent for each catalog is significantly larger compared withthat for the stocks included in the catalog. Selecting a window with size650, theevolution of scaling for the Shanghai Stock Index is obtained by the window’s slidingalong the series. We can find that the important events fit very well with globaltransitions of the scaling behaviors. Find three break point of market structure.