How to interpret the results of the cointegration test?

How to interpret the results of the cointegration test?

In order to interpret our cointegration results, let’s revisit the two steps of the Engle-Granger test: Estimate the cointegration regression. Test the residuals from the cointegration regression for unit roots. The Engle-Granger test statistic for cointegration reduces to an ADF unit root test of the residuals of the cointegration regression:

How does the Engle Granger cointegration test work?

The Engle-Granger Cointegration Test The Engle-Granger cointegration test considers the case that there is a single cointegrating vector. The test follows the very simple intuition that if variables are cointegrated, then the residual of the cointegrating regression should be stationary. Forming the cointegrating residual

Which is the leading case of the cointegrating equation?

In the leading case, is simply the number of cointegrating variables (including the dependent) in the system, but the value must generally account for deterministic trend terms in the system that are excluded from the cointegrating equation. The bottom section of the output depicts the results for the actual ADF test equation:

How is normalization used in the cointegration test?

In the two-stage, residual-based cointegration tests which we will consider today, normalization amounts to deciding which variable is our dependent variable and which variables are our independent variables in the cointegration regression.

Which is the cointegration rank equal to one?

This translates into cointegration rank being equal to one (number of variables in the system minus the number of cointegrating vectors: $3-2=1$). Two cointegrating vectors is not the same as cointegration order being equal to two.

Can you reject the null of no cointegration?

Cannot reject the null of no cointegration for A D F, Z t, or Z α. Cannot reject the null of no cointegration for A D F, Z t, or Z α. Cannot reject the null of no cointegration for A D F, Z t, or Z α. Cannot reject the null of no cointegration for A D F, Z t, or Z α.

How does Phillips-Ouliaris test for no cointegration?

More importantly, the test statistics show that, as with the Engle-Granger tests, the Phillips-Ouliaris tests reject the null hypothesis of no cointegration (unit root in the residuals) at roughly the 1% significance level. The intermediate results are given by: There are a couple of new results.

How to interpret Johansen cointegration test EViews results?

“The report shows that “None” is not being rejected ” – you could not reject “no cointegration” (In other words, your null hypothesis is “no cointegration” and you failed to reject it/you accept it, meaning that there is no cointegration).

How is the Johansen test for cointegrating time series analysis?

The logic is that all three should in some part be affected by stochastic trends in commodities and thus may form a cointegrating relationship. In Ernie’s work he carried out the Johansen procedure using MatLab and was able to reject the hypothesis of r ≤ 2 at the 5% level.

How to interpret results of Johansen test in R?

I am using urca package of R. Here is the summary of test (trace test with constant intercept): ca.jo (cbind (a,b), type=”trace”, ecdet = “const”, K = 2, spec =”longrun”) Test type: trace statistic , without linear trend and constant in cointegration

When to use a cointegration test for structural breaks?

In the case that structural breaks have occurred, standard tests for cointegration are invalid. Therefore, it is important to: Test whether structural breaks occur in the individual series. In the case that there is evidence of structural breaks, employ cointegration tests that allow for structural breaks.

When does the Johansen test check for no cointegration?

The test checks for the situation of no cointegration, which occurs when the matrix A = 0. The Johansen test is more flexible than the CADF procedure outlined in the previous article and can check for multiple linear combinations of time series for forming stationary portfolios. To achieve this an eigenvalue decomposition of A is carried out.

Which is more likely to reject the null hypothesis of no cointegration?

Therefore, the Engle-Granger test considers the null hypothesis that there is no cointegration. As the Engle-Granger test statistic decreases: We are more likely to reject the null hypothesis of no cointegration. We have stronger evidence that the variables are cointegrated.