Engle Granger Test for Cointegration

Overview


The cointegrating relationship is
{% y_t = \beta_0 + \beta_1x_{1,t} + ... + \beta_nx_{n,t} + \mu_t %}
where {% \mu_t %} is that a stationary time series, given by
{% \mu_t = y_t - \beta_0 - \beta_1x_{1,t} - ... - \beta_nx_{n,t} %}
{% \mu %} is often referred to as the error correction. That is, it represents the deviation from the equilibrium relationship. Being stationary, it is guaranteed to drift back toward equilibrium over time.

Steps


  1. Test that {% y %} and {% x %} are I(1) (integrated order 1. That is, stationary after differencing)
  2. Run a regression on the cointegrating equation above
  3. Verify that the residuals are stationary


While the standard unit root tests can be used to test that the residuals are stationary, it is not entirely correct. This is due to the fact that the cointegrating equation and its coefficients used in the test are only estimated values.

Engle and Granger estimated a new set of critical values to used when testing unit roots of the residuals.