Quantile Regression Estimation Of Network GARCH(1,1) Model

Network and Network Analysis is one of the rapidly developing fields in recent years.At the same time,in the financial field,more and more financial data need to establish the Generalized autoregressive conditional heteroscedasticity(GARCH)model and analyze.However,the GARCH model is mainly applicable to univariate time series data.Portfolio optimization and risk management in the real capital market usually require a variety of different stock combinations.Therefore,the combination of network and financial time series data has attracted the interest of many scholars.In the past,when estimating the parameters of the model,the conditional expectation of the dependent variable is studied,but people also concerned about the relationship between the independent variable and the quantile of the dependent variable distribution.In order to comprehensively describe the full picture of conditional distribution of dependent variables,many scholars conducted quantile regression and analysis on financial time series models.In this paper,we first give some preliminary knowledge,including the definition and properties of GARCH model,the advantages and properties of quantile regression,ideas and methods of GARCH model for quantile regression.On this basis,we introduce the network GARCH model.In order to simplify the research,the quantile estimation of network GARCH(1,1)model is transformed into a simple linear quantile regression problem by function transformation.Secondly,we study and discuss the asymptotic properties of the estimated value.Then we use computer to simulate the model,and show that the modeling ability of network GARCH(1,1)model is good.Finally,we collected the closing prices of 21 banks and constructed the network GARCH(1,1)model to verify the practicability of the model.