What is an error correction model (ECM)?

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AcadiFi · Accepted Answer

An error correction model represents the short-run dynamics of cointegrated series, with an additional term that pulls the system back toward its long-run equilibrium. The ECM says changes in the series depend on past changes and on the deviation from equilibrium. For two cointegrated series y and x, the ECM is: delta y_t equals alpha plus sum of lagged delta terms plus lambda times (y_{t-1} minus beta times x_{t-1}) plus epsilon_t. The key coefficient lambda is the error correction speed: the fraction of last period's equilibrium deviation corrected this period. It must be negative and statistically significant for the ECM to be valid — otherwise the system does not actually error-correct and the relationship is not truly cointegrating. Example: analyst Remigio Paternoster at Colosseo Macro Research models Italian BTP yields (y) and German Bund yields (x). Cointegration is established. The estimated ECM shows lambda equals negative 0.14 with t-stat negative 3.8. Interpretation: each week, about 14 percent of the deviation from the long-run spread is corrected, implying a half-life of roughly five weeks. ```mermaid flowchart LR D[Deviation
from eq] --> L[lambda
negative] L --> C[Correction
next period] C --> R[Return to
equilibrium] ``` Granger's representation theorem guarantees that if two series are cointegrated, an ECM representation exists. ECMs are standard tools for monetary policy analysis, yield curve modeling, and exchange rate econometrics.

What is an error correction model (ECM)?

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