ARResults.wald_test(r_matrix, cov_p=None, scale=1.0, invcov=None, use_f=None, df_constraints=None)

Compute a Wald-test for a joint linear hypothesis.

r_matrixarray-like, str, or tuple
  • array : An r x k array where r is the number of restrictions to test and k is the number of regressors. It is assumed that the linear combination is equal to zero.

  • str : The full hypotheses to test can be given as a string. See the examples.

  • tuple : A tuple of arrays in the form (R, q), q can be either a scalar or a length p row vector.

cov_parray-like, optional

An alternative estimate for the parameter covariance matrix. If None is given, self.normalized_cov_params is used.

scalefloat, optional

Deprecated since version 0.10.0.

Default is 1.0 for no scaling.

invcovarray-like, optional

A q x q array to specify an inverse covariance matrix based on a restrictions matrix.


If True, then the F-distribution is used. If False, then the asymptotic distribution, chisquare is used. If use_f is None, then the F distribution is used if the model specifies that use_t is True. The test statistic is proportionally adjusted for the distribution by the number of constraints in the hypothesis.

resContrastResults instance

The results for the test are attributes of this results instance.


The matrix r_matrix is assumed to be non-singular. More precisely,

r_matrix (pX pX.T) r_matrix.T

is assumed invertible. Here, pX is the generalized inverse of the design matrix of the model. There can be problems in non-OLS models where the rank of the covariance of the noise is not full.