statsmodels.sandbox.sysreg.SUR¶
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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.
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cholsigmainv
¶ The transpose of the Cholesky decomposition of pinv_wexog
Type: array
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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: array
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df_resid
¶ Residual degrees of freedom of each equation. Number of observations less the number of parameters.
Type: array
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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: array
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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: array
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history
¶ Contains the history of fitting the model. Probably not of interest if the model is fit with igls = False.
Type: dict
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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: array
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pinv_wexog
¶ The pseudo-inverse of the wexog
Type: array
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sigma
¶ M x M covariance matrix of the cross-equation disturbances. See notes.
Type: array
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sp_exog
¶ Contains a block diagonal sparse matrix of the design so that exog1 … exogM are on the diagonal.
Type: CSR sparse matrix
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wendog
¶ M * nobs x 1 array of the endogenous variables whitened by cholsigmainv and stacked into a single column.
Type: array
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wexog
¶ M*nobs x sum(p_{m}) array of the whitened exogenous variables.
Type: array
Notes
All individual equations are assumed to be well-behaved, homoeskedastic 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 initialize
()predict
(design)whiten
(X)SUR whiten method.