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

$$-\frac{n}{2}\log \left({(Y-\hat{Y})}^{\prime }(Y-\hat{Y})\right)-\frac{n}{2}(1+\log \left(\frac{2\pi }{n}\right))-\frac{1}{2}\log \left(\left|\mathrm{\Sigma }\right|\right)$$

Y and Y-hat are whitened.