Macro-econometrics assignment - construct the daily return

Question

Macro-Econometrics Assignment -

The data set NYSE.XLS contains a series called COMPOSITE, which are the daily closing values for the NYSE index from January 3, 1995 to August 30, 2002. The following exercises follow those in section 10 of the textbook.

(a) Construct the daily return as r_t = ln(COMPOSITE_t) - ln(COMPOSITE_t-1). Graph the series. Do you think it makes sense to model this series assuming a constant conditional mean for this sample of data? What about the conditional variance? Why not?

(b) Begin by estimating a MA(2) model for the conditional mean and a constant conditional variance.

r_t = μ₀ + ε_t + δ₁ε_t-1 + δ₂ε_t-2

Save the residuals from the above regression and create another series where the residuals are squared. Now test for time-varying variance by running the following regression:

ε_t² = α₀ + α₁ε_t-1² + α₂ε_t-2² + α₃ε_t-3² + α₄ε_t-4²

where the terms in the regression are the squared-residuals from your MA(2) regression. What is the F-statistic associated with the null hypothesis that all of the coefficients on the lagged variables are equal to zero? Can you reject this hypothesis? If so, what does this mean?

(c) Now re-estimate the MA(2) model, but use an GARCH(1,1) model for the conditional variance:

h_t = α₀ + αε_t-1² + βh_t-1

What are estimates do you obtain for α and β? How do you interpret them in light of this example (stock market returns and volatility)? What do you notice about the estimates of the MA terms compared to the results in (b)?

(d) Now estimate a ARCH-M model for the conditional mean and a GARCH(1,1) model for the conditional variance:

r_t = μ₀ + ε_t + δ₁ε_t-1 + δ₂ε_t-2 + γh_t

h_t = α₀ + αε_t-1² + βh_t-1

What estimated value do you obtain for γ? How do you interpret this coefficient in light of this example? Does it have the "right" sign? Is it significantly different from zero?

(e) The models estimated above do not represent a systematic study of how to model NYSE returns. Very briefly describe what steps you would take to make such a study.

Please attach the relevant code or STATA/R/Eviews output.

Attachment:- Assignment Files.rar