Time-Varying Network Methods Research And Applications In Capital Market

The network topology of complex systems is an important method to study the interaction between individuals in complex systems.In the field of statistical machine learning,undirected graphs are the main theoretical models for studying the topology of a network.For undirected graphs model with continuous variables,Gaussian Markov graphs are the main theoretical model.Most of the literature focuses on the estimation of static Gaussian undirected graph models.However,in real network systems,the connectivity between nodes and nodes tends to change slowly with the passage of time.This paper assumes that the connectivity of each node reflected by the data generated by network nodes at different time points changes with time.In this paper,the method proposed by Zhou(2010)is introduced to give different weights to the data at different time points,which solves the problem of lacking data to estimate the time-varying network structure.When estimating network structure at each time point,this paper focus on the GLasso algorithm proposed by O'Banerjee et al.(2007)and R.Tibshirani et al.(2008),and according to the idea of GLasso's improvement proposed by R.Mazumder and T.Hastie et al.(2012),this paper proposed a specific solution using a coordinate method to solve the optimization problem in the improvement idea.Statistical simulation studies the accuracy of the time-varying network estimation method of time-weighted adjustment and the advantages of the improved estimation algorithm for GLasso's estimation algorithm.In the empirical part,by analyzing the meaning of the network topology changing with time,this paper correlates the dynamic change of the stock time-varying network with the expectation of the investors in the capital market.Combined with the traditional event analysis framework,The meeting held the overall impact on the stock market after the policy incident.