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Vector Error Correction Model (VECM)

Also known as: vector error correction model, error correction model, cointegration model, VECM (Vektör Hata Düzeltme Modeli)

OriginatorEngle & GrangerYear1987Sources1Related methods9

The Vector Error Correction Model is a multivariate time-series model for cointegrated series that captures both their short-run dynamics and their long-run equilibrium relationship. It was introduced by Engle and Granger in 1987 as part of the cointegration and error-correction framework.

Key highlights

  • Models short-run dynamics and the long-run equilibrium relationship jointly in one framework.
  • Built for cointegrated I(1) series, avoiding the spurious-regression problem of running levels in OLS.
  • The adjustment coefficients reveal how fast each series returns to equilibrium after a shock.

Intuition

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How it works

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When to use it

Use VECM when you have several continuous time series that are individually non-stationary integrated of order one (I(1)) but move together in a long-run equilibrium, that is, they are cointegrated as confirmed by the Johansen test. It is suited to both forecasting and studying relationships among the series, and works best with a reasonably long sample (at least about 60 observations). If the series are not cointegrated, a plain VAR in differences is more appropriate; in small samples the ARDL bounds test is more reliable.

Strengths & limitations

Strengths
  • Models short-run dynamics and the long-run equilibrium relationship jointly in one framework.
  • Built for cointegrated I(1) series, avoiding the spurious-regression problem of running levels in OLS.
  • The adjustment coefficients reveal how fast each series returns to equilibrium after a shock.
Limitations
  • Requires cointegration: if none exists the error-correction term is meaningless and a VAR should be used instead.
  • Needs all series to be integrated of the same order, I(1).
  • The cointegration coefficients are biased in small samples (n < 60), where the ARDL bounds test is more dependable.

Common pitfalls

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Applications

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Frequently asked

What is the difference between VECM and VAR?

A VAR models the joint dynamics of several time series without imposing a long-run relationship. A VECM is a restricted VAR for cointegrated I(1) series that adds an error-correction term capturing the long-run equilibrium. If the series are not cointegrated, use a VAR (typically in differences); if they are, VECM is preferred.

How do I know if my series are cointegrated?

Use the Johansen test, which also tells you the cointegration rank, the number of independent long-run relationships. Cointegration requires the series to be integrated of order one (I(1)) and to share a stationary linear combination.

What does the error-correction term mean?

It measures how far the system is from its long-run equilibrium in the previous period. Its coefficient (the adjustment speed α) shows what fraction of that disequilibrium is corrected in the current period, pulling the series back toward equilibrium.

What should I do if there is no cointegration?

If the Johansen test finds no cointegration, the error-correction term is meaningless. Estimate a VAR in differences instead. In small samples (n < 60), consider the ARDL bounds test, which is more reliable for detecting long-run relationships.

Sources

  1. 1.
    Engle, R. F. & Granger, C. W. J. (1987). Co-Integration and Error Correction: Representation, Estimation, and Testing. Econometrica, 55(2), 251-276.
    DOI 10.2307/1913236

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ScholarGate. (2026, June 1). VECM. ScholarGate. https://scholargate.app/econometrics/vecm-model

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