I have read Vidyamurthy and others, but did not find clear example of error correction model (ECM) application in pairs trading.

How should I use the ECM model in the pairs trading?

How to use ECM coefficients "speed with which the time series corrects itself to maintain equilibrium", a_x and a_y?

  • $\begingroup$ Please provide a link to your reference formula/variables $\endgroup$
    – rrg
    Commented Oct 12, 2016 at 19:10
  • $\begingroup$ yes, please elaborate a little more, otherwise I will vote to close your question $\endgroup$
    – lehalle
    Commented Oct 13, 2016 at 9:41

1 Answer 1


If (x, y) are both integrated to the same order (commonly I(1)), we can estimate an ECM model of the form: ${\displaystyle A(L)\Delta y_{t}=\gamma +B(L)\Delta x_{t}+\alpha (y_{t}-\beta _{0}-\beta _{1}x_{t})+\nu _{t}}$

Estimate the model using Ordinary least squares: ${\displaystyle y_{t}=\beta _{0}+\beta _{1}x_{t}+\epsilon _{t}}$

Then the predicted residuals ${\displaystyle {\hat {\epsilon _{t}}}=y_{t}-\beta _{0}-\beta _{1}x_{t}}$ from this regression are saved and used in a regression of differenced variables plus a lagged error term:

${\displaystyle A(L)\Delta y_{t}=\gamma +B(L)\Delta x_{t}+\alpha {\hat {\epsilon _{t-1}}}+\nu _{t}} $.

This completes the error correction method. In practice the widespread uses of ECM in equity pairs has made the revenue potential either tiny or redundant.

Also see https://en.wikipedia.org/wiki/Error_correction_model#An_example_of_ECM for a consumption ECM example.


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