# What is Johansen cointegration test for?

## What is Johansen cointegration test for?

Johansen’s test is a way to determine if three or more time series are cointegrated. More specifically, it assesses the validity of a cointegrating relationship, using a maximum likelihood estimates (MLE) approach.

### How do you know if variables are cointegrated?

Two sets of variables are cointegrated if a linear combination of those variables has a lower order of integration. For example, cointegration exists if a set of I(1) variables can be modeled with linear combinations that are I(0).

#### How the Engle Granger eg test can be used to find out if two or more time series are cointegrated?

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.

**What is the Johansen test in statistics?**

The Johansen tests are likelihood-ratio tests. There are two tests: 1. the maximum eigenvalue test, and 2. the trace test. For both test statistics, the initial Johansen test is a test of the null hypothesis of no coin- tegration against the alternative of cointegration.

**What is the Johansen test for cointegration?**

The rank of the matrix A is given by r and the Johansen test sequentially tests whether this rank r is equal to zero, equal to one, through to r = n − 1, where n is the number of time series under test. The null hypothesis of r = 0 means that there is no cointegration at all.

## How do you perform a Johansen test on a matrix?

To achieve this an eigenvalue decomposition of A is carried out. The rank of the matrix A is given by r and the Johansen test sequentially tests whether this rank r is equal to zero, equal to one, through to r = n − 1, where n is the number of time series under test. The null hypothesis of r = 0 means that there is no cointegration at all.

### What are the eigenvalues in Johansen’s test?

To repeat, the eigenvalues used in Johansen’s test are not eigenvalues of the matrix directly, although the eigenvalues in the test also can be used to determine the rank of and have tractable distributions. The eigenvalues are guaranteed to be non-negative and real.