statsmodels.tsa.ar_model.ARResults.cov_params

ARResults.cov_params(r_matrix=None, column=None, scale=None, cov_p=None, other=None)

Returns the variance/covariance matrix.

The variance/covariance matrix can be of a linear contrast of the estimates of params or all params multiplied by scale which will usually be an estimate of sigma^2. Scale is assumed to be a scalar.

Parameters:
  • r_matrix (array-like) – Can be 1d, or 2d. Can be used alone or with other.
  • column (array-like, optional) – Must be used on its own. Can be 0d or 1d see below.
  • scale (float, optional) – Can be specified or not. Default is None, which means that the scale argument is taken from the model.
  • other (array-like, optional) – Can be used when r_matrix is specified.
Returns:

cov – covariance matrix of the parameter estimates or of linear combination of parameter estimates. See Notes.
Return type:

ndarray

Notes

(The below are assumed to be in matrix notation.)

If no argument is specified returns the covariance matrix of a model (scale)*(X.T X)^(-1)

If contrast is specified it pre and post-multiplies as follows (scale) * r_matrix (X.T X)^(-1) r_matrix.T

If contrast and other are specified returns (scale) * r_matrix (X.T X)^(-1) other.T

If column is specified returns (scale) * (X.T X)^(-1)[column,column] if column is 0d

OR

(scale) * (X.T X)^(-1)[column][:,column] if column is 1d