Regression analyses on non-stationary time series rise the need to test for cointegration. A set of time series are said to be cointegrated, if there exists stationary linear combination amongst them (Engle and Granger, 1987). There are two strains of cointegration test provided by i-Regand: (1) residual based and (2) rank test or widely known as Johansen’s cointegration test.

For the former, i-Regand provides ADF and Phillips tests. They are basically unit root tests applied to residual of a regression. Hence, they test whether or not the residual is non-stationary. If the residual is stationary, then there exists cointegration amongst non-stationary variables involved in the regression.

The later takes totally different way of doing the test. As proposed by Johansen (1991), a VAR of non-stationary series contains cointegrating relationships if the long-run matrix has neither zero rank nor full rank. If it has zero rank, then there is no cointegration and regression should be carried out on first differences. If it is full rank, then all of the variables are stationary. Thus, the number of cointegrating vector, if any, must be at least one, but less than the number of variables. This is the advantage of Johansen test, it can identify the number of cointegrating relations.

## ADF cointegration test

ADF cointegration test is an ADF unit root test applied to the residual of a regression. Note that the residual represents a linear combination of variables involved in the regression. Thus, stationarity of the residual indicates the existence of a cointegrating relationship. The test takes non-stationarity (no cointegration) as the null hypothesis. The steps to carry out ADF unit-root test are:

Step 1. Tap on the main menu and select ADF cointegration test

Step 2. Specify the variable involved in the regression

Step 3. Specify the lag selection criteria and input the maximum lag

Step 4. Run and see the results

The results display test statistics from three models: CONSTANT (model with constant), TREND (model with constant and trend), QUAD (model with constant, trend, and quadratic trend). Each of them is accompanied with 1%, 5%, and 10% critical values (negative). If the ADF statistic is more than the critical value, the residual is non-stationary and hence there is no cointegration. There is also information about optimal lag chosen by the Apps.

## Phillips cointegration test

The Phillips cointegration test applies kernel whitening procedure to remove nuisance parameters from the residual. There are also three models: CONSTANT, TREND, QUAD. The steps to carry out Phillips cointegration test are:

Step 1. ap on the main menu and select Phillips cointegration test

Step 2. Specify the variables involved in the regression

Step 3. Specify the kernel and bandwidth selection criteria

Step 4. Run and see the results

The results are similar to the ADF test and therefore no further explanation is needed.