VAR and VECM
Model interacting time series and equilibrium adjustment
A VAR models each variable using lags of all variables in a system. A VECM reparameterises a cointegrated VAR into changes and long-run equilibrium errors. Reduced-form innovations capture statistical surprises; structural shocks require additional identifying restrictions. Impulse responses and forecast-error decompositions therefore depend on model specification and the chosen identification scheme.
Use for interacting time series, multivariate forecasting or dynamic responses when the sample supports the number of equations and lags. Use a VECM when cointegration should be retained explicitly.
Strengths
- Models feedback among variables rather than one equation alone
- Separates short-run dynamics from long-run adjustment in a VECM
Limitations
- Parameter counts grow quickly with variables and lags
- Structural interpretations depend on additional identification assumptions
Know the boundary
A Cholesky ordering is an identifying assumption, not a discovered causal ordering. A VECM is specifically a cointegrated-system representation.