Generalized Least Squares-
If the off-diagonal elements
of covariance matrix of the residuals with its lag are not 0, then there can be
correlation across cases.
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
https://drive.google.com/file/d/0Bx3mfFH5R-y3ZVJkNnV1bDBTUWs/view?usp=sharing
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