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.