Generalized Least Square

          Generalized Least Squares- 

GLM does not assume a linear relationship between dependent and independent variables.

If the off-diagonal elements of covariance matrix of the residuals with its lag are not 0, then there can be correlation across cases.

In a time-series problem, that amounts to autocorrelation and Generalized least square is used.

-        Estimation of Ὠ for GLS-

Heteroscedasticity-

                     1-    By OLS calculate error terms.

Y = X β + u, u ~(0, Ὠ)

Let  be the OLS residuals. The goal is to use the residuals to construct a consistent estimate of Ὠ.

                2-    Ὠ = Covariance matrix of residuals with its lags. 

 

         E.g-  Excel Sheet - 
 https://drive.google.com/file/d/0Bx3mfFH5R-y3ZVJkNnV1bDBTUWs/view?usp=sharing