Applying an Error Correction Model to Pairs Trading

Summary

The document outlines a two-step way to apply an error correction model to a candidate pair of nonstationary price series. It assumes the series are integrated to the same order, commonly first order. First, estimate a long-run relationship by regressing one series on the other and retain the residuals, which represent deviations from that fitted equilibrium. Then regress changes in one series on lagged changes in both series and the lagged residual from the long-run fit. The coefficient on that residual captures adjustment toward the estimated relationship in the specified equation.

This gives a basic model specification, not a complete trading system. The response does not show how to select lags, test cointegration, estimate both legs' adjustment speeds, or translate estimates into entries, exits, and risk controls. It also cautions that widespread use of ECM methods in equity pairs may leave little or no trading opportunity. That statement is not supported with performance evidence in the exchange, so practical profitability remains unestablished.

Key ideas

• An error correction model can be considered when both series share the same integration order.
• Estimate the long-run relationship first and retain its residuals as deviations from equilibrium.
• Use lagged residuals alongside differenced variables in the short-run regression.
• The adjustment coefficient describes how the modeled series responds to the prior period's equilibrium error.
• The outline omits trading rules and cautions that common use may limit opportunities.

Tags

# How can I apply error correction model in pairs trading?


# How can I apply error correction model in pairs trading?












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?

## Answer by rrg (score 2)

https://quant.stackexchange.com/a/30525

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.

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.