# Engle Granger Test

The Engle Granger test is a test for cointegration. It constructs residuals (errors) based on the static regression. The test uses the residuals to see if unit roots are present, using Augmented Dickey-Fuller test or another, similar test. The residuals will be practically stationary if the time series is cointegrated.

## Engle Granger Test Procedure

The null hypothesis for the Engle Granger test is that no cointegration exists. The null hypothesis is written, using standard hypothesis testing notation, as:

H0: No cointegration exists

The alternate hypothesis is that the series has cointegration of some kind. It can be written as:

H1: Cointegration exists

The Engle Granger test can be performed in MATLAB (with egcitest) or STAT (using the egranger command).

In R:

2. Follow the instructions to run the test on this page. The following image shows the first part of the instructions (scroll down about half way to Cointegration: Engle-Granger Test),

## Improvements on the Engle Granger Tests

Johansen’s Test is another improvement over the Engle-Granger test. It avoids several issues, including having to choose a dependent variable and carrying errors from one step to the next. Johansen’s is more suited to multivariate analysis than Engle Granger, because it can detect multiple cointegrating vectors. Gonzalo & Lee (1997) note that Engle-Granger tends to be more robust than Johansen’s likelihood ratio test, so they recommend using both Engle-Granger and Johansen tests to weed out any potential problems.

Prior to 1987, tests for cointegration worked on the assumption that regression errors are independent with common variance—which is rarely true in real life (Chaovalitwongse et. al, 2010). The Philips-Ouliaris test (1990) is a newer, residual-based unit root test that may be used in place of Engle Granger. In general, the test performs as well or better than the E-G, but—as all of these tests can be a little finicky&mdsh; you may want to run multiple tests and compare the results.

## References

Armstrong, J. Principles of Forecasting: A Handbook for Researchers and Practitioners. Springer Science & Business Media
Chaovalitwongse, W. et. al (2010). Computational Neuroscience. Springer Science & Business Media.
Rao, B. (2007). Cointegration: for the Applied Economist, Springer.