ARBIMETRA LAB
VECM
Models cointegrated series, reporting long-run relations, adjustment speeds and short-run dynamics.
What it does
Models cointegrated series, reporting long-run relations, adjustment speeds and short-run dynamics.
Use it after finding cointegration.
Data you need
- Two to four cointegrated series
Supported data: Time series. Level: Advanced.
Formula and method
Δyₜ = αβ′yₜ₋₁ + ΣΓᵢΔyₜ₋ᵢ + uₜ
Given a cointegration rank, maximum likelihood estimates the long-run vectors β and adjustment speeds α jointly with short-run dynamics, and the model is reported in error-correction form.
Assumptions
- Series are I(1) and cointegrated at the chosen rank
Input checks
- Two to four series
How to read the result
Adjustment coefficients show which series responds to long-run deviations.
Worked example
Illustrative run on US quarterly macro 1959-2009. These figures are the actual output of this model on that example, and they say nothing about your own data.
- Rank 1, 3 short-run lag(s), 199 observations.
- Significant adjustment: realcons (EC1: 0.0331, p = 0.0007)
- A significant adjustment coefficient shows which variable moves to restore the long-run relationship. A variable with no significant adjustment is weakly exogenous to that relationship.
Limitations
- Results depend on the sample period
Numerical validation
Validated 16 of 16 automated checks passed, including numerical results, invalid input, missing values, small samples, constant variables, charts and the interpretation text.
| Check | Reference | Result | Abs. error | Tolerance | Source |
|---|---|---|---|---|---|
| Recovers the known long-run relation | -0.5 | -0.49510118 | 4.9e-3 | 5e-2 | Known data-generating value |
| Long-run combination is stationary around a mean | 1 | 1 | 0.0e+0 | 0e+0 | Known data-generating value |
Computed with python 3.13.2, numpy 2.2.5, scipy 1.14.1, pandas 2.3.3, statsmodels 0.14.4, scikit-learn 1.7.0, in your browser. A passing check confirms the listed comparison only. It does not make any result suitable for your data, and it is not a claim of equivalence with other statistical software.
Questions
When should I use VECM rather than VAR?
When the series are non-stationary and cointegrated.
ARBIMETRA LAB is an educational and research tool. Results should be checked by the researcher and are not professional advice.