A CAPM beta with a -statistic of 3.2 makes a claim about sampling uncertainty. That claim depends on the regression model and its covariance estimate. Crisis volatility, overlapping returns, parameter breaks, and correlated factors each create a different problem. This lesson separates those problems and chooses the corresponding diagnostic or repair. It starts from ordinary least squares; efficiency improvements from covariance-based weighting belong to GLS.
Learning objectives. By the end of this note you should be able to:
- state the classical linear regression model and assumptions A1–A6, and prove the conditional OLS variance under spherical errors;
- state Gauss–Markov and name which finance facts break which assumptions;
- construct White's test and HC standard errors; distinguish HC from HAC;
- run Durbin–Watson and Breusch–Godfrey screens and state the Newey–West idea;
- derive simple omitted-variable bias, interpret RESET and Chow, and compute VIF;
- execute a factor-regression diagnostic checklist and choose classical, HC, or HAC inference — or rebuild the mean.
In this lesson
- The classical linear model
- OLS and Gauss–Markov
- Where finance breaks the assumptions
- Heteroscedasticity: White and HC
- Serial correlation: DW, Breusch–Godfrey, Newey–West
- Specification: RESET, omitted variables, dummies, Chow
- Multicollinearity and VIF
- Worked walkthrough: diagnosing a factor regression
Before you start
- Simple Linear Regression: OLS Estimators and Geometry
- Multiple Linear Regression
- Inference in Simple Linear Regression
The full lesson, with worked examples and exercise solutions, is for members.
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