Research On Unit Root Tests Under A Structural Break Or With EGARCH Errors

Using traditional limited theorems to non-stationary time series gives misleading inference, and econometrics and traditional statistics methods are failure to non-stationary time series,which are applied by econometrics data in recent years.Granger and Newbold had put forward a new question,which was called by spurious regression from 1974,then research on non-stationary is a hot topic.Because stationary time series and non-stationary time series come form different data generating processes,they have different contents,properties and analysis technique.The testing of stationary behavior of time series is a precondition to mathematical modeling.Testing for the presence of a unit root is that testing time series are stationary or non-stationary.Unit root process is one of non-stationary processes.The theories of unit root processes in financial time series have received a great amount of attention in terms of theoretical and applied research over decades.In order to distinguish between unit root processes and stationary processes better,the difference between the trend stability processes and unit root with intercept processes by monte carlo simulation is shown in chapter one of this paper.Viewed from the nature of the graphs,the difference is studied in more details in terms of the stabilization method,the convergence speed of estimate and the distribution of statistics and so on.Unit root test is a basic way to estimate stationary behavior of financial time series.There is an error that traditional unit root tests are used for unit root process of time series with a possible change in its intercept or slope.The situation of exogenous structural break are subjective and if unit root processes of time series with a possible change in its intercept or slope aren't in accord with the fact,the power of tests is false.In chapter two of this paper,we select the break point using the methodologies of endogenously structural break tests for time series,which are made by the form of structural break model through Hodrick-Prescott filter,followed by the ADF tests in an exogenous break are used.The results of the simulation analysis are illustrated efficiently via an application,which is more effective than exogenously structural break tests.The first problem in ADF tests is that we should take into account the effect,which has been produced by various parameters of unit root processes with GARCH-error on critical value,power and size.The effects are analyzed,which show that the critical values using traditional ADF tests under t or GED conditional distribution of the error term in GARCH model.GARCH model is widely applied to financial economics,which has characterized explicitly economic variable data. However,GARCH model doesn't indicate leverage effect and persistence in volatility of conditional heteroscedasticity.To improve it,Nelson presented EGARCH model in 1991,which improved the forecasting precision and played an important role in financial volatility study.In the paper chapter three,firstly we demonstrate the result about the limited distribution of test statistics with lag based on Functional Central Limit Theorem,and then we simulate ADF unit root test of finite sample time series under EGACH with norm,t or GED distribution of the error term using WLS and OLS methods.The critical value,exact size,power and the critical values of statistics of various lag order are analyzed.The conclusion is that WLS method is superior to OLS and statistics t((?)) is an effective contrast to statistics t_?.