Unit Root And Cointegration Tests Of Time-varying Variance And Applications

The theory and application of unit root and cointegration tests are the main research fields of macro econometrics theory and application.This paper analyzes the unit root,cointegration,and panel unit root test theories of time-varying variance in this frontier.Monte Carlo simulation is used to explore the finite sample properties of unit root and cointegration test in time-varying variance.At the same time,this paper applies the above tests reasonably and accurately to the relevant variables of China’s capital and energy markets.It not only verifies and promotes the theory of unit root and co-integration test of time-varying variance from the perspective of actual data but also is consistent in theoretical application.Firstly,this paper interprets the unit root test theory of time-varying variance,explores its limited sample property,and uses the example of investor sentiment to verify its validity.This paper firstly uses the Global Database of Events,Language and Tone(GDELT)to obtain millions of news media reports and constructs the news media sentiment of the Chinese stock market based on the textual analysis method.The news media sentiment proposed in this paper is logically consistent in its definition and characteristics.Meanwhile,the paper applies the Wild Bootstrap unit root test based on time-varying variance to construct the stationarity test of news media sentiment.It concludes that news media sentiment is a random walk process with time-varying variance.From the perspective of econometric theory,this paper confirms the conclusion that investor sentiment cannot have long-term pricing ability.Then,this paper interprets the residual cointegration test theory under time-varying variance,explores its limited sample property,and verifies the validity of the test with an example of the short-term and long-term relationship between investor sentiment and turnover rate.Firstly,the cointegration test based on residuals under time-varying variance is used to analyze the Chinese stock market’s investor sentiment and turnover rate.It is concluded that there is a long-term cointegration relationship between news media sentiment and the turnover rate of the stock market.Secondly,the threshold variable is added to explore the asymmetric impact of positive and negative news media sentiment on the turnover rate based on the traditional error correction model.The results show a shortterm dynamic relationship between investor sentiment and turnover rate.The average recovery speed of turnover rate is significantly different with the positive or negative mood.This provides theoretical evidence for the asymmetric influence of investor sentiment on the turnover rate in the stock market.Finally,this paper interprets the panel unit root test theory of time-varying variance,explores its limited sample property,and verifies the validity of the test by using the energy efficiency panel data at the prefecture-level.In this paper,environmental factors are first introduced into the study of energy efficiency,and the SBM-Undesirable model is used to incorporate industrial "three wastes" and greenhouse gases into the measurement of energy efficiency to calculate the panel data of green total factor energy efficiency and energy intensity at 267 prefecture-level in China during 2005-2019.Further,to explore the evolution and convergence mode of China’s urban energy efficiency gap,this paper investigates the regional differences in China’s energy efficiency based on the stochastic convergence method.It analyzes the convergence and dispersion of energy efficiency between regions from the perspective of the panel unit root test of time-varying variance.This paper attempts to provide a theoretical basis for answering whether the energy efficiency of cities in eastern,western,and central China converges or diverges.The conclusion provides theoretical support for the policy suggestion of realizing the energysaving target of the 14 th Five-Year Plan.