statsmodels.regression.linear_model.GLSAR.loglike¶
-
GLSAR.
loglike
(params)¶ Compute the value of the Gaussian log-likelihood function at params.
Given the whitened design matrix, the log-likelihood is evaluated at the parameter vector params for the dependent variable endog.
- Parameters
- paramsarray_like
The model parameters.
- Returns
float
The value of the log-likelihood function for a GLS Model.
Notes
The log-likelihood function for the normal distribution is
\[-\frac{n}{2}\log\left(\left(Y-\hat{Y}\right)^{\prime} \left(Y-\hat{Y}\right)\right) -\frac{n}{2}\left(1+\log\left(\frac{2\pi}{n}\right)\right) -\frac{1}{2}\log\left(\left|\Sigma\right|\right)\]Y and Y-hat are whitened.