Analysis of Financial Time Series, Third Edition

2.10 Consistent Covariance Matrix Estimation

Consider again the regression model in Eq. (2.43). There may exist situations in which the error term et has serial correlations and/or conditional heteroscedasticity, but the main objective of the analysis is to make inference concerning the regression coefficients α and β. See Chapter 3 for discussion of conditional heteroscedasticity. In situations under which the OLS estimates of the coefficients remain consistent, methods are available to provide consistent estimate of the covariance matrix of the coefficient estimates. Two such methods are widely used. The first method is called the heteroscedasticity consistent (HC) estimator; see Eicker (1967) and White (1980). The second method is called the heteroscedasticity and autocorrelation consistent (HAC) estimator; see Newey and West (1987).

For ease in discussion, we shall rewrite the regression model as

2.48

where yt is the dependent variable, is a k-dimensional vector of explanatory variables including constant, and is the parameter vector. Here denotes the transpose of the vector