While there is a large literature on cointegrating regressions with near unit root regressors, the focus has been on inference on the slope parameter in these. Phillips 1987 showed that the sample moments of yt. To estimate the slope coefficients, one should first conduct a unit root test, whose null hypothesis is that a unit root is present. The adequate procedure usually involves the specification of a data dependent algorithm to find out whether or not a breaking point is present in the data, and in which period of the sample it is located. I selected the series as a group, then specified the po test option, and here is the output. Stationarity and unitroot testing why do we need to test for nonstationarity. You must specify either the dfuller or the pperron option. Phillipsperrontype unit root tests in the nonlinear estar. Accordingly, the next three pages contain the relevant statistical tables for dickeyfuller and phillips. Asymptotic properties of residual based tests for cointegration. However, there remain many ways to use the defactored residuals to construct a test. The stationarityor otherwise of a series can strongly influence its behaviour and properties e.
The phillips perron test phillips and perron have developed a more comprehensive theory of unit root nonstationarity. Phillips and sam ouliaris 1990 show that residualbased unit root tests applied to the estimated cointegrating residuals do not have the usual dickeyfuller distributions under the null hypothesis of nocointegration. A note on phillips perrontype statistics for cointegration testing. In the panel unit root test framework, two generations of tests have been developed. Unit root and cointegration tests for time series data rdrr. Stationarity and unit root testing why do we need to test for nonstationarity. Stationarity, johansens test, phillipouliaris method, stock price, unit root. Due to the spurious regression phenomenon under h0, the distribution of the adf and pp unit root tests have asymptotic. A residualbased test of the null of cointegration against the alternative of no. Testing for cointegration errorcorrection representation testing for cointegration when is unknown key results.
Two new tests are also introduced, one of which is invariant to the normalization of the cointegrating regression. Phillips and ouliaris propose a bounds procedure based upon the corresponding. Phillips and ouliaris po 1990 show that the adf and pp unit root tests applied to the estimated cointegrating residual do not have the usual df distributions under h0 nocointegration. The adf and pp test specified for this study are given in eq 8 and. More importantly, the test statistics show that, as with the englegranger tests, the phillips ouliaris tests reject the null hypothesis of no cointegration unit root in the residuals at roughly the 1% significance level. As we discussed before, if one of the rjs equals 1. The testing procedure for the adf unit root is used to the model. All of these tests are shown to be asymptotically similar and.
Phillips and ouliaris po 1990 show that the adf and pp unit. Title unit root and cointegration tests for time series data. Moreover, they contain critical values for only a few. The stationarity or otherwise of a series can strongly influence its behaviour and properties e. However, if the presence of a unit root is not rejected, then one should apply the difference operator to the series. Although they are based on simulation, they should be. This is like a multivariate version of the adf test. Values of h equal to 0 indicate a failure to reject the unit root null. The unit root is estimated from a regression of the first variable column of x on the remaining variables of x without a constant and a linear trend. A unit root test is a statistical test for the proposition that in a autoregressive statistical model of a time series, the autoregressive parameter is one. The englegranger and phillips ouliaris residualbased tests for cointegration are simply unit root tests applied to the residuals obtained from sols estimation of equation 27. Classes for time series data standard time series class in r is ts. The change over the following time unit also distributed as n0,1.
In conclusion, we reject the null hypothesis that the residuals have unit roots, therefore the series are cointegrated. It builds on the dickeyfuller test of the null hypothesis in. Pdf exploring the methods of cointegration procedures using. Since our null hypothesis is cointegration rather than no cointegration, our cointegration test does not suffer from the conceptual pitfalls indicated by phillips and ouliaris 27. The phillips perron zalpha statistic for a unit root in the residuals of the cointegration regression is computed, see also pp. The name comes from the method it uses, which is called phillipsouliaris. That is, it is used in time series analysis to test the null hypothesis that a time series is integrated of order 1.
For example, when there is no trend in the cointegration regression, the 5% critical value of the englegranger test is3. Rs ec2 lecture 16 1 1 lecture 16 unit root tests a shock is usually used to describe an unexpected change in a. A residualbased test of the null of cointegration against. Aimed at regular series annual, quarterly, monthly. Vector of pvalues of the test statistics, with length equal to the number of tests. Several statistical tests for unit roots have been developed to test for. Pdf testing for a unit root in time series regression. The complete set of phillipsouliaris critical values distinguish between whether or.
The stationarity or otherwise of a series can strongly influence its behaviour and properties. The first part of the unit root output provides information about the form of the test the type of test, the exogenous variables, and lag length used, and contains the test output, associated critical values, and in this case, the pvalue. Asymptotic properties of residual based tests for cointegration authors. Values of h equal to 1 indicate rejection of the unit root null in favor of the alternative model. Therefore, a test of the null hypothesis of no cointegration. In statistics, the phillips perron test named after peter c. If two variables are trending over time, a regression. It is well known that the limiting distribution of the leastsquares estima. Critical values for cointegration tests queens university. In statistics, the phillipsperron test named after peter c. The null hypothesis in the englegranger procedure is nocointegration and the alternative is. A note on phillipsperrontype statistics for cointegration.
Adf test on the ordinary least squares ols residuals from a regression of one. Unit root, differencing the time series, unit root test adf. Such procedure transforms perrons unit root test, which is conditional on a known breakpoint, into an unconditional unit root test. A ts object is either a numeric vector univariate series or a. Vector of boolean decisions for the tests, with length equal to the number of tests.
Afurtherinvestigation jushan bai and serena ng columbia university an effective way to control for crosssection correlation when conducting a panel unit root test is to remove the common factors from the data. You must specify either the pperron or the dfuller option. The tests are similar to adf tests, but they incorporate. Phillips and ouliaris po 1990 show that is not the case. A study of cointegration models with applications by rajab ssekuma submitted in accordance with the requirements for the degree of master of commerce in the subject statistics at the university of south africa supervisor. Dec 21, 2012 hi guys i am looking for assistance with the phiilipsouilaris test for cointegration of two series. Ouliaris1 this paper develops an asymptotic theory for residual based tests for cointegration.
This paper provides tables of critical values for two versions of the eg test and three versions of the df test. Im trying to implement cointegration tests using the r urca package. The limiting nonstandard distributions are derived under very gen. Phillips and ouliaris 1990 show that residualbased unit root tests applied to the estimated cointegrating residuals donothave the usual dickeyfuller distributions under the null hypothesis of nocointegration. Unit root test, take home message it is not always easy to tell if a unit root exists because these tests have low power against nearunitroot alternatives e. Conducts the johansen procedure on a given data set. Under the assumption that the series are not cointegrated, all linear combinations of, including the residuals from sols, are unit root nonstationary.