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.
- sigmaarray_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.
- sys
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)
- Attributes
- 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.
- cholsigmainv
Methods
fit
([igls, tol, maxiter])igls : bool
predict
(design)whiten
(X)SUR whiten method.