statsmodels.sandbox.sysreg.SUR¶

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

Seemingly Unrelated Regression

Parameters:¶

syslist

[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

dfkNone, ‘dfk1’, or ‘dfk2’

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

Attributes:¶

cholsigmainvndarray

The transpose of the Cholesky decomposition of pinv_wexog

df_modelndarray

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_residndarray

Residual degrees of freedom of each equation. Number of observations less the number of parameters.

endogndarray

The LHS variables for each equation in the system. It is a M x nobs array where M is the number of equations.

exogndarray

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.

historydict

Contains the history of fitting the model. Probably not of interest if the model is fit with igls = False.

iterationsint

The number of iterations until convergence if the model is fit iteratively.

nobsfloat

The number of observations of the equations.

normalized_cov_paramsndarray

sum(p_{m}) x sum(p_{m}) array \(\left[X^{T}\left(\Sigma^{-1}\otimes\boldsymbol{I}\right)X\right]^{-1}\)

pinv_wexogndarray

The pseudo-inverse of the wexog

sigmandarray

M x M covariance matrix of the cross-equation disturbances. See notes.

sp_exogCSR sparse matrix

Contains a block diagonal sparse matrix of the design so that exog1 … exogM are on the diagonal.

wendogndarray

M * nobs x 1 array of the endogenous variables whitened by cholsigmainv and stacked into a single column.

wexogndarray

M*nobs x sum(p_{m}) array of the whitened exogenous variables.

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
initialize()
predict(design)
whiten(X)	SUR whiten method.