In this chapter, students will be able to understand: Describe the steps involved in testing regression residuals for heteroscedasticity and autocorrelation, explain the impact of heteroscedasticity or autocorrelation on the optimality of OLS parameter and standard error estimation, distinguish between the Durbin-Watson and Breusch-Godfrey tests for autocorrelation,. | Chapter 5 Classical linear regression model assumptions and diagnostics ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 1 Violation of the Assumptions of the CLRM • Recall that we assumed of the CLRM disturbance terms: 1. E(ut ) = 0 2. var(ut ) = σ 2 < ∞ 3. cov(ui ,uj ) = 0 4. The X matrix is non-stochastic or fixed in repeated samples cov(ut ,xt ) = 0 5. ut ∼ N(0, σ 2 ) ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 2 Investigating Violations of the Assumptions of the CLRM • We will now study these assumptions further, and in particular look at: – How we test for violations – Causes – Consequences in general we could encounter any combination of 3 problems: – the coefficient estimates are wrong – the associated standard errors are wrong – the distribution that we assumed for the test statistics will be inappropriate – Solutions – the assumptions are no longer violated – we work around the problem so that we use alternative techniques which are still valid ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 3 Statistical Distributions for Diagnostic Tests • Often, an F- and a χ2 - version of the test are available. • The F-test version involves estimating a restricted and an unrestricted version of a test regression and comparing the RSS. • The χ2 - version is sometimes called an “LM” test, and only has one degree of freedom parameter: the number of restrictions being tested, m. • Asymptotically, the 2 tests are equivalent since the χ2 is a special case of the F-distribution: χ2 (m) → F (m, T − k) as m (T − k) → ∞ • For small samples, the F-version is preferable. ‘Introductory Econometrics for Finance’ c Chris Brooks 2013 4 Assumption 1: E (ut ) = 0 • Assumption that the mean of the disturbances is zero. • For all diagnostic tests, we cannot observe the disturbances and so perform the tests of the residuals. • The mean of the residuals will always be zero provided that there is a constant term in the .
