class statsmodels.sandbox.sysreg.SUR(sys, sigma=None, dfk=None)[source]

Seemingly Unrelated Regression


sys : list

[endog1, exog1, endog2, exog2,...] It will be of length 2 x M, where M is the number of equations endog = exog.

sigma : array-like

M x M array where sigma[i,j] is the covariance between equation i and j

dfk : None, ‘dfk1’, or ‘dfk2’

Default is None. Correction for the degrees of freedom should be specified for small samples. See the notes for more information.


All individual equations are assumed to be well-behaved, homoeskedastic iid errors. This is basically an extension of GLS, using sparse matrices.

\sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M}\\
\sigma_{21} & \sigma_{22} & \cdots & \sigma_{2M}\\
\vdots & \vdots & \ddots & \vdots\\
\sigma_{M1} & \sigma_{M2} & \cdots & \sigma_{MM}\end{array}\right]


Zellner (1962), Greene (2003)


cholsigmainv array The transpose of the Cholesky decomposition of pinv_wexog
df_model array Model degrees of freedom of each equation. p_{m} - 1 where p is the number of regressors for each equation m and one is subtracted for the constant.
df_resid array Residual degrees of freedom of each equation. Number of observations less the number of parameters.
endog array The LHS variables for each equation in the system. It is a M x nobs array where M is the number of equations.
exog array The RHS variable for each equation in the system. It is a nobs x sum(p_{m}) array. Which is just each RHS array stacked next to each other in columns.
history dict Contains the history of fitting the model. Probably not of interest if the model is fit with igls = False.
iterations int The number of iterations until convergence if the model is fit iteratively.
nobs float The number of observations of the equations.
normalized_cov_params array sum(p_{m}) x sum(p_{m}) array \left[X^{T}\left(\Sigma^{-1}\otimes\boldsymbol{I}\right)X\right]^{-1}
pinv_wexog array The pseudo-inverse of the wexog
sigma array M x M covariance matrix of the cross-equation disturbances. See notes.
sp_exog CSR sparse matrix Contains a block diagonal sparse matrix of the design so that exog1 ... exogM are on the diagonal.
wendog array M * nobs x 1 array of the endogenous variables whitened by cholsigmainv and stacked into a single column.
wexog array M*nobs x sum(p_{m}) array of the whitened exogenous variables.


fit([igls, tol, maxiter]) igls : bool
whiten(X) SUR whiten method.

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