Analysis Of Stock Market Features Based On High-dimensional Volatility Network Model

At present,the global economic and political structure is still in the process of indepth adjustment.Unilateral trade and protectionist sentiment have intensified,and the possibility of "peaking down" in the world economic growth has increased.Affected by the external environment,some deep-seated contradictions have gradually emerged which has accumulated over the course of China's economic development.Economic growth faces increasing difficulties,and financial risks are prone to occur and showing new characteristics and evolutionary trends.Financial markets are highly sensitive to external shocks,and the risk of abnormal market fluctuations cannot be ignored.Under the current complex domestic and international economic situation and the background of the era of big data,it is particularly important to better measure and mine the fluctuations and risk characteristics of the stock market.Volatility plays a crucial role in the field of financial risk management.The traditional volatility model is limited by the dimension of the variable.It cannot effectively solve the problem that the increase of the dimension of the model variable caused by the increase in the number of assets.Therefore,it cannot fully utilize the financial big data to describe the market's operating characteristics in detail which pose new challenges on volatility modeling and risk management in the era of big data.This paper proposes a high-dimensional volatility network model for the stock market based on complex network theory and data mining technology.First,the Pearson correlation coefficient and mutual information are utilized to measure the correlation of stock price fluctuations,and we research on the applicability of the two in measuring the correlation of stock price volatility.Second,with the distance matrix transformed by correlation coefficient,minimum spanning tree network and threshold network are built on the realized volatility and realized range to analyze the network topological characteristics such as the degree centralization,average distance,power law distribution and aggregation coefficient for different periods of the stock market.Finally,the Fast Unfolding algorithm is used to stratify the correlation of the volatility.The empirical results demonstrate that in contrast to the Pearson correlation coefficient,non-linear correlation of stock volatility is well measured by mutual information.The market volatility and price volatility correlation move in the opposite direction,and the portfolio decentralization effect is more obvious in the period of high market volatility.The effects of industry agglomeration are significant.The volatility network is scale-free network and there exist a small number of key nodes and central nodes in the network,and the risk quickly spreads to the entire market through these nodes.The network stratification further shows the characteristics of risk transmission between layers and corresponding industrial characteristics which provide powerful data support and path guidance for investors in asset portfolio allocation and managers in risk management.The high-dimensional volatility network model proposed in this paper mainly has three advantages: First,the model belongs to a non-parametric estimation model,there is no complicated parameter estimation process,and it is not limited by variable dimensions like the construction of traditional multivariate volatility models.Second,the high-dimensional volatility network model is not limited to reflecting the relationship between any two variables in isolation,but can also intuitively and comprehensively reflect the role of each variable in the process of variable relationship transmission and the network topology of the financial market in the form of a network topology diagram.Third,the existing financial market theories mostly rely on various hypotheses,and the high-dimensional volatility network can explore and study the interrelationships among the main bodies of the financial market relying less on hypotheses.The high-dimensional volatility network model provides a new perspective and tool for mining stock market risk characteristics and financial risk management.