CAPM-GARCH - Regression analysis with heteroskedasticity

Okay, it seems to work with Mahalanobis:
b = (X?S^?1X)?1X?S^?1Y minimizes the Mahalanobis-distance of Xb to Y .
And S is the covariance-matrix. 

cov = a0+a1x_{n-1}*y_{n-1}+?*cov{n-1}
But shouldn?t it be the covariance of the residuals?

Anyone experiences with that?

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