| In the context of economic globalization,the impact of changes in the stock market can have political,cultural and social implications.Stock returns and asset pricing are the main time-series objects of research in finance,and volatility is an important indicator to characterize this uncertainty,and the more popular research direction is to model the conditional variance.The impact of the market on returns is usually asymmetric,and with this leverage effect,how to accurately characterize and predict returns has become a major concern for stock buyers and sellers and managers.Asymmetric financial data are common,multivariate GARCH models are popular,and it is challenging to make statistical inferences for high-dimensional problems.Complex network analysis provides a new approach to the study of complex systems in society,and network analysis has become a popular research direction.Various studies have shown that adding network structure can improve models,and it is an important approach to multivariate problems,providing new ways to further address volatility problems.This paper proposes a network APGARCH model,which adds a network structure to the APGARCH model to greatly reduce the number of parameters and the complexity of computation.Firstly,the definition of the model and its strict stationarity are proposed,then the quasi-maximum likelihood estimation is introduced and the consistence and asymptotic normality of the parameters are obtained;secondly,numerical study is divided into two parts,one is the numerical simulation.The simulated data were generated by setting three different network structures with random distribution,power-law distribution and random block model,and then the parameters were estimated by using the proposed maximum likelihood estimation method to verify the finite sample nature of the model;the other part is the example analysis.The other part is the example analysis.First,we test for missing data,outliers and ARCH effects.After that,three network structures were set up to analyze the actual stock data of 30 banks using common shareholder information,and the results were tested by residual analysis to prove the usefulness of the model.The out-of-sample prediction part is compared with the APGARCH model,thus proving the usefulness of the model.Then,the theorems of strict stationarity and asymptotic normality are proved.Finally,a conclusion and outlook are given. |
