DeGroote School of Business
Due March 22, 5pm.
Hand in a pdf copy of your computer output and a separate write-up of the answers
to the following questions to Avenue, Assignment 2 by 5pm March 22. Each student’s
write-up should be done independently. Using the same data and model as assignment
RGEt = α + βRMt + γSMBt + δHMLt + ut, ut ∼ NID(0, σ2), (1)
answer the following questions.
1. (20) Test for second order autocorrelation in the error terms and ARCH(2) het-
eroskedasticity. Report your findings.
2. (20) Based on your results in (a) report valid estimates and t-statistics for the
3. (30) Test for a structural break in all regressor coefficients assuming a break point
at January 2007, the start of the financial crisis. Keep in mind your results from
4. (30) Estimate the following model with ARCH(2) using maximum likelihood and
by extending the code mle arch.r and mle oil gdp.r. Report estimates, standard
errors, z-stats for each coefficient being 0 and the log-likelihood value. Mention any
difficulties in estimation and convergence. Is there evidence of heteroskedasticty?
Perform an LR test for this. The model is
RGEt = β1 + β2RMt + β3SMBt + β4HMLt + ut, (2)
ut = σtzt zt ∼ NID(0, 1), (3)
σ2t = α0 + α1u
t−1 + α2u
where α0 > 0, α1 ≥ 0, α2 ≥ 0. Parameters to estimate are β1, β2, β3, β4, α0, α1, α2.