Vector Error Correction Model (VECM)

A vector error correction model (VECM) is a multivariate time series model for cointegrated variables that captures both short-run dynamics and the speed of adjustment back to a long-run equilibrium.

벡터오차수정모형(VECM)은 공적분된 변수들에 대해 단기 동학과 장기 균형으로 되돌아가는 조정 속도를 함께 포착하는 다변량 시계열 모형이다.

How do I model short-run and long-run relationships among several cointegrated time series?

공적분된 여러 시계열 사이의 단기 및 장기 관계를 어떻게 모형화하나요?

A vector error correction model estimates long-run cointegrating relationships together with short-run changes and error correction terms that show how quickly variables return to equilibrium. It fits multiple nonstationary series that the Johansen test finds to be cointegrated.

When to use Vector Error Correction Model (VECM)

• Two or more I(1) series with at least one cointegrating relationship
• Estimating the speed of adjustment to long-run equilibrium
• Macroeconomic or financial systems such as prices, rates and output

When to use something else

• The series are stationary in levels: use a vector autoregression (VAR) model
• Series are nonstationary but not cointegrated: use a VAR in first differences

Assumptions and requirements

• Variables integrated of order one
• Cointegration confirmed (e.g., Johansen trace and maximum eigenvalue tests)
• Appropriate lag length chosen by information criteria
• Residuals free of autocorrelation

What the analysis reports

• Johansen test results and cointegration rank
• Cointegrating vectors (long-run coefficients)
• Adjustment (error correction) coefficients
• Short-run coefficients
• Impulse response functions

How to report it

The Johansen trace test indicated [r] cointegrating relationship(s), and the error correction term for [variable] was negative and significant, α = [value], p = [value].

Related methods

• Vector Autoregression (VAR)
• Johansen Cointegration Test
• Granger Causality Test

Run Vector Error Correction Model (VECM) on Quorant