Seemingly Unrelated Regression
Parameters: | sys : list
sigma : array-like
dfk : None, ‘dfk1’, or ‘dfk2’
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Notes
All individual equations are assumed to be well-behaved, homoeskedastic iid errors. This is basically an extension of GLS, using sparse matrices.
\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]
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. |
Methods
fit([igls, tol, maxiter]) | igls : bool |
initialize() | |
predict(design) | |
whiten(X) | SUR whiten method. |
Methods
fit([igls, tol, maxiter]) | igls : bool |
initialize() | |
predict(design) | |
whiten(X) | SUR whiten method. |