A Method Of Nonstationary Time Series Analysis Based On “The Degree Of Cointegration”:The Equal Variance Test And Its Applications

Since the 1970 s,the nonstationary time series analysis had become an important footstone in modern Econometrics.Many marco-economic and financial variables have been confirmed to be nonstationary,hence could be described by unit root processes.Due to the spurious regression problem,to detect the stationarity of the variables using unit root tests is alomot a requested step before we begin to analyze the data.However,structural breaks can affect the performance of unit root tests dramatically.It is therefore important to study the effect of structural breaks on unit root tests,how and how serious structural breaks affect the performance of the unit root tests.Given the variables being nonstationary,cointegration is the tool to analyze the relatioonships between nonstationary variables.Unfortunately,cointegration can only detect whether or not the variables are cointegrated,which is very restrictive in applications.We first examine the main literature on the nonstationary time serires analysis and extract the limitations of theoretical framework in modern Econometrics.Then,using research methods composed of deriving asymptotic theories,Monte Carlo simulatons and empirical analysis,we show how structural breaks affect the Dickey-Fuller unit root tests,and recommend an effective solution.Based on the existed theory,we define the degree of cointegration to extend the cointegration,and construct the equal variance test to determine the degree of cointegration.Finally,we show the usefulness of the degree of cointegration by studying several economic problems.Particularly,the dissertation includes the following parts:1.By deriving the asymptotic theory,we show how omitting the existed Fourier-form breaks affects the Dickey-Fuller test,i.e.,we show that the asymptotic distribution is invariant to Fourier-form breaks.Monte Carlo simulations are conducted to examine the asymptotic theory and its predictions.Simulations also show that Fourier function augmented Dickey-Fuller test has satisfying performance under the smooth breaks and the abrupt breaks.So,this study can fill up the blank of the existed theory,support the use of Fourier function augmented Dickey-Fuller test and help us understand the Dickey-Fuller test.2.Under the framework of cointegration,we define the concept of the degree of cointegration and provide the meaning of it.The new concept can extend the cointegration theory.The equal variance test,which accommodates the cross-setional dependence,is proposed to determine the degree of cointegration,which therefore can be labelled as the test of the degree of cointegration.The equal variance test are shown to be robust to serial correlation and cross-sectional dependence.Its finite sample performance is assessed by Monte Carlo simulations.Using the similar method,the equal mean test are proposed and shown to have good performance.The framework of examining the degree of cointegration are extended to dynamic framework,and the conditions where the equal variance test is available are derived.3.To examine the usefulness of the proposed method,the new concept and equal variance test are used to study several empirical problems: the comovements between Chinese stock market and international stock market,the influence of China and the effect of the stock future on the stock market volatility.These applications are shown to be helpful to answer some economic problems.Therefore,the degree of cointegration and the equal variance test are confirmed to be useful and meaningful.Finally,by using the degree of cointegration and the equal variance test,an investment strategy is discussed.We show the difference between the analysis based on the degree of cointegration and the analysis based on returns.The new method is useful at least as a supplement to the traditional analysis based on returns.