Skip to content
All library documents

Why the Engle–Granger Procedure Estimates an Error-Correction Model

Article Quant Q&A · Author: GC2023
Read the original

Summary

The document asks how the error-correction model (ECM) fits into the two-step Engle–Granger test for bivariate cointegration and pairs trading. The author understands the first step as regressing one series on the other to estimate the cointegrating coefficient, then applying an augmented Dickey–Fuller test to the residuals. The question is whether this already establishes cointegration and supplies the beta needed for a trading strategy.

It contrasts this understanding with a cited pairs-trading paper that reportedly estimates an ECM in the second step, and asks what that model adds or how its estimates should be used. The document provides no answer or empirical results. It raises a useful distinction between testing for a long-run relationship and modeling short-run adjustment, but does not resolve whether the OLS coefficient alone is sufficient for the paper’s implementation.

Key ideas

  • The first Engle–Granger step estimates a long-run coefficient by regressing one series on another.
  • The residual-based augmented Dickey–Fuller test is used to assess whether the residual relationship is stationary.
  • The author asks what estimating an ECM adds after the cointegration test and coefficient estimate.
  • The document does not explain the ECM’s role or prescribe how to use its estimates in a trading strategy.

Tags

Pairs tradingStatisticsMean reversion
Full text
# What do I need the Error correction model for in the two step Engle Granger approach (bivariate Cointegration)


# What do I need the Error correction model for in the two step Engle Granger approach (bivariate Cointegration)












could someone kindly explain what I need the ECM for in a bivariate Cointegration test?

I am currently trying to reproduce the results of Rad et al. (2015): "The profitability of pairs trading strategies: distance, cointegration, and copula methods".

For the implementation of the Cointegration pairs trading strategy, the two step Engle Granger procedure is used. I understand that first, I can estimate the cointegration coefficient beta by doing an OLS estimation by regressing y(t) on x(t). In the case of bivariate cointegration, the OLS estimator would be superconsistent. Therefore, I understand that I need to test for Cointegration next, using the ADF test on the residuals. If the ADF test now tells me that the residuals are stationary and thus y(t) and x(t) are cointegrated, I would assume, that I proved that the two variables are cointegrated and I do also already have my coefficient beta. I do not understand why I should still estimate an ECM, or what I should use the estimated ECM for respectively, because in the paper, it seems like they only test for cointegration and use beta fom then. However, they say that they use the Engle Granger two step method and estimate the ECM in the second step.

I could imagine that for some reason, I cannot use the beta estimated with OLS. Is that true? And if so, why can't I use it if it is superconsistent and tends to the true value?

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.