A factor regression gives less precise information on high-volatility days. Robust standard errors describe that uncertainty without changing the OLS coefficients. Generalised least squares changes the weights instead. It can improve precision when the disturbance covariance is known or credibly estimated. This lesson derives that transformation, calculates a weighted factor regression, and explains the risks of estimated weights.
Learning objectives. By the end of this note you should be able to:
- write the GLS estimator and its covariance for known positive definite ;
- derive GLS as OLS on a transformed equation with ;
- recognise WLS as the diagonal case and compute a small weighted factor regression;
- explain why OLS remains consistent under exogeneity while classical SEs fail;
- state the two-step logic of feasible GLS and its main caveats.
In this lesson
- The problem OLS does not solve
- GLS for known
- Why classical OLS standard errors fail
- Weighted least squares: the diagonal case
- GLS for AR(1) disturbances (sketch)
- Feasible GLS
- Decision table
Before you start
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