statsmodels.sandbox.sysreg.SUR¶
- class statsmodels.sandbox.sysreg.SUR(sys, sigma=None, dfk=None)[source]¶
Seemingly Unrelated Regression
- Parameters:
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.
- cholsigmainv¶
The transpose of the Cholesky decomposition of pinv_wexog
- Type:
ndarray
- df_model¶
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.
- Type:
ndarray
- df_resid¶
Residual degrees of freedom of each equation. Number of observations less the number of parameters.
- Type:
ndarray
- endog¶
The LHS variables for each equation in the system. It is a M x nobs array where M is the number of equations.
- Type:
ndarray
- exog¶
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.
- Type:
ndarray
- history¶
Contains the history of fitting the model. Probably not of interest if the model is fit with igls = False.
- Type:
- normalized_cov_params¶
sum(p_{m}) x sum(p_{m}) array \(\left[X^{T}\left(\Sigma^{-1}\otimes\boldsymbol{I}\right)X\right]^{-1}\)
- Type:
ndarray
- pinv_wexog¶
The pseudo-inverse of the wexog
- Type:
ndarray
- sigma¶
M x M covariance matrix of the cross-equation disturbances. See notes.
- Type:
ndarray
- sp_exog¶
Contains a block diagonal sparse matrix of the design so that exog1 … exogM are on the diagonal.
- Type:
CSR sparse matrix
- wendog¶
M * nobs x 1 array of the endogenous variables whitened by cholsigmainv and stacked into a single column.
- Type:
ndarray
- wexog¶
M*nobs x sum(p_{m}) array of the whitened exogenous variables.
- Type:
ndarray
Notes
All individual equations are assumed to be well-behaved, homoskedastic iid errors. This is basically an extension of GLS, using sparse matrices.
\[\begin{split}\Sigma=\left[\begin{array}{cccc} \sigma_{11} & \sigma_{12} & \cdots & \sigma_{1M}\\ \sigma_{21} & \sigma_{22} & \cdots & \sigma_{2M}\\ \vdots & \vdots & \ddots & \vdots\\ \sigma_{M1} & \sigma_{M2} & \cdots & \sigma_{MM}\end{array}\right]\end{split}\]References
Zellner (1962), Greene (2003)
Methods
fit([igls, tol, maxiter])igls : bool
predict(design)whiten(X)SUR whiten method.
