Statistical Network Analysis Of Stock Markets During Financial Turbulence

In this research,we have attempted to analyze a real-world problem,the volatility of financial markets,using network theory,and create a specific framework to interpret it.In this study,along with the theoretical investigation of the problem,we consider practical aspects of it to help the financial market actors to have a better understanding of the topological structure of the stock market.Due to the nonlinearity nature of the financial markets,unlike the usual methods,information theory is used to build networks and to define the distance between companies in the constructed networks.After reviewing the research background and available literature,the turbulence of the Chinese financial market that emerged over the years,2015-2016 is considered the primary source of the review.US financial market turbulence at the same time is also deployed to examine and compare the results with the results of Chinese financial market networks.Using the Symbolization method of time series,Mutual Information(MI)is used to construct the Minimum Spanning Trees(MST),Distance Covariance(DC)also deployed to to examine the results obtained from Mutual Information based networks.We construct three minimum spanning trees of pre-turbulence,turbulence and post-turbulence using MI and DC methods.The findings show that minimum spanning tree of turbulence has the significant differences in topological characteristics and network’s measures with pre-turbulence networks in both data sets of Chinese and US stock markets using MI and DC methods.The network measures of different period such as degree ratio,betweenness,closeness,eigenvector centrality,node eccentricity,node strength,node domination compared with the measures of the other two periods.Results show that there are significant differences among some of the measures between different periods.For example In Chinese stock market network constructed by MI,the eigenvector centrality of turbulence is less than other two periods.Betweenness centrality of MST has decreased during the turbulence,but approximately the same during pre-turbulence and post-turbulence.Closeness centrality of the nodes during turbulence is greater than the closeness of the two other periods.The eccentricity of the companies during preturbulence and post-turbulence is greater than the MST of turbulence.The strength of nodes during the turbulence is less than pre-turbulence and post-turbulence.For S&P stock price networks constructed by MI and Distance Covariance the same results are observed.But the topological structure and the dominated companies are different in both constructed networks.Another significant result obtained in this study for the MSTs constructed by MI and DC for both types of data is that with removing random nodes the stock correlation networks of pre-turbulence display the topological robustness but turbulence MST is fragile against randomly node’s failure.The last part of this dissertation,which is perhaps the most important as well as the extracts from the previous sections,is about defining an autoregressive model using network theory.In this section,we have tried to draw on all of the previously mentioned tools to develop a model based on network theory to solve the issues of multivariate analysis for analysing the financial markets.The proposed model is based on three essential effects.First,the impact of yesterday’s stock price of a company on today’s stock price of a company which we call it previous time effect.Second,the effect of the network of other stock prices on a specific stock price which we call it market effect.Third,the impact of independent noise.These effects,with its coefficients,linearly build our SPNAR model.Compared with other modeling approaches such as multivariate time series,which model each company individually where relationship across different companies is lost,SPNAR model is constructed to handle these issues.The results show that the accuracy and performance of this model are more than some time series models like Autoregressive(AR),Moving Average(MA),Autoregressive Moving Average(ARMA),and Vector Autoregressive(VAR)models.Furthermore,the parameter estimation in SPNAR model is more convenient and feasible than time series models as mentioned earlier.Moreover,In this study,the characteristics of three various periods,pre-turbulence,turbulence,and post-turbulence are analyzed,and findings show there is a significant difference between turbulence period with other periods in topological structure and the behavior of the networks.