Theoretical Frontier Extensions And Applications Of Unit Root And Cointegration Tests

It is well known that the study of unit root and cointegration is one of the most popular fields of econometric theory.Based on analyzing the recent literature in this field,we develop new theory and methods for unit root and cointegration tests.The standard unit root test,e.g.,ADF(Dickey&Fuller,1979;Said&Dickey,1984)and PP(Phillips&Perron,1988)tests,assume that the parameters in the data generating process remain unchanged.However,a large number of articles demonstrate that many key macroeconomic and financial variables are characterized by permanent volatility shifts,and that the adjustment to the long-term equilibrium is non-linear and asymmetric.Therefore,this paper develops a new AESTAR unit root test under time-varying variance.This paper investigates the effects of time-varying variance on the traditional AESTAR unit root test.We derive the limiting null distributions of the statistics under time-varying variance,which are shown to be different significantly from those derived in the case of constant variance.We propose a wild bootstrap-based implementation of the test and prove that the wild bootstrap statistics share the same limiting null distributions as the original statistics,so that the bootstrap procedure is asymptotically valid.We develop a new dependence robust AESTAR unit root test,which combined with the wild bootstrap approach,is proven to be valid in the presence of both time-varying variance and weak dependence.Monte Carlo simulations show our procedure works well in finite samples.We apply our proposed method to test the Purchasing Power Parity(PPP)hypothesis for Asian countries and regions,and find that our proposed test provides stronger evidence against the PPP hypothesis than the conventional AESTAR test.This evidence offers a new view for the PPP test.Correctly specifying the deterministic trend in a time series variable is very important for unit root tests.Testing for the existence of a linear trend also has many interesting economic interpretations.Recently,Harvey,Leybourne and Taylor(2007,hereafter denoted as HLT)and Perron and Yabu(2009,hereafter denoted as PY)propose two robust linear trend tests,which are groundbreaking solutions to this problem.However,HLT and PY both assumed the variance of the series to be constant.We investigate the impact of time-varying variance on the HLT and PY linear trend tests,and derive the limiting null distributions of the HLT and PY linear trend tests,which are different from normal distributions derived under constant variance assumption.We propose two new linear trend tests using the long run variance estimator proposed by Xu(2010).We demonstrate that under time-varying variance the limiting null distributions of our proposed tests are standard normal distributions,regardless of whether the variable is I(1)or 1(0).Monte Carlo simulations show that HLT and PY have severe size distortions,but our proposed tests perform well in finite samples.We apply the new tests to examine the existence of the deterministic trend in Chinese CPI.The results show that there is no linear time trend in Chinese CPI.The Johansen cointegration test is the most widely used cointegration test method in empirical research.However,the Johansen cointegration test proposed by Johansen(1996)assumed that the deterministic trend has no structural change,i.e.,the intercept and slope coefficients of the deterministic trend in the VECM model are constant,and that the variance of the errors of the VECM model remains unchanged.We propose a new cointegration test in VECM model with a broken linear trend and time varying variance.We allow multiple structural changes in deterministic trend,but assume the break dates in deterministic trend are known.We assume that the variance of the errors of the VECM model is time-varying,thereby allows a very wide class of permanent variance changes which includes single and multiple volatility breaks.We derive the limiting null distributions of the cointegration test statistics under broken linear trend and time-varying variance,which are shown to be different significantly from those derived in the case of constant variance.We propose a wild bootstrap-based implementation of the cointegration test and prove that the wild bootstrap cointegartion test statistics share the same limiting null distributions as the original statistics,so that the bootstrap procedure is asymptotically valid.Monte Carlo evidence suggests that the proposed wild bootstrap cointegration tests work very well in finite samples.Identifying the structural shocks in the cointegration VECM model has important economic applications.Based on the KPSW method(King et al.,1991),we can identify the permanent shocks and transitory shocks in the VECM model,and then decompose the variables into long term trend and transitory component.This paper,based on the cointegration among GDP,consumption,investment and net export in China,decomposes Chinese GDP into long-term trend and transitory component.According to the evolution of long-term trend,this paper makes inference on the quantitative characteristics of Chinese economy's "new normal".The main results are the following.The growth rate of the long-term trend of Chinese GDP is shifting down.Its average growth rate is reduced from 9.88%in 2001-2009 to 7.85%in 2010-2014.This result not only reveals the sources of continuous fall in economic growth since 2010,but also shows the necessity of China's economic slowdown.The transitory component of GDP represents the changes of money,expection and other short term factors.The slowdown of GDP growth rate is the outcome of the declining of the long term trend and transitory component.The results show that it is important to promote the long term gowth factors so as to increase the trend growth rate.Appropriate stimulation policy is also needed to prevent the transitory component of GDP slowdown.