statsmodels.tsa.vector_ar.vecm.coint_johansen

statsmodels.tsa.vector_ar.vecm.coint_johansen(endog, det_order, k_ar_diff)[source]

Perform the Johansen cointegration test for determining the cointegration rank of a VECM.

Parameters:
  • endog (array-like (nobs_tot x neqs)) – The data with presample.
  • det_order (int) –
    • -1 - no deterministic terms
    • 0 - constant term
    • 1 - linear trend
  • k_ar_diff (int, nonnegative) – Number of lagged differences in the model.
Returns:

result – An object containing the results which can be accessed using dot-notation. The object’s attributes are

  • eig: (neqs)

    Eigenvalues.

  • evec: (neqs x neqs)

    Eigenvectors.

  • lr1: (neqs)

    Trace statistic.

  • lr2: (neqs)

    Maximum eigenvalue statistic.

  • cvt: (neqs x 3)

    Critical values (90%, 95%, 99%) for trace statistic.

  • cvm: (neqs x 3)

    Critical values (90%, 95%, 99%) for maximum eigenvalue statistic.

  • method: str “johansen”

  • r0t: (nobs x neqs)

    Residuals for \(\Delta Y\). See p. 292 in [1].

  • rkt: (nobs x neqs)

    Residuals for \(Y_{-1}\). See p. 292 in [1].

  • ind: (neqs)

    Order of eigenvalues.
Return type:

Holder

Notes

The implementation might change to make more use of the existing VECM framework.

References

[1](1, 2) Lütkepohl, H. 2005. New Introduction to Multiple Time Series Analysis. Springer.