Description
GX5004 HW 5
1. Consider the AR(1) DGP presented in class: �! = ��!!! + �!.
a. For this exercise, set � = 0.5. Generate this DGP using 1,000 Gaussian white-noise
draws from N(0,1) by letting �! = �!. Plot this DGP. Run a linear regression to get the
least-squares estimate of �. (You should include a constant in the regression.) Does
your 95% confidence interval include 0.5?
b. Repeat a. assuming � = −0.5.
c. Repeat a. assuming � = 1. (This is called a random walk or unit root.)
d. Submit code and results.
2. In this exercise, you will work with two independent random walks.
a. Following 1c. above, generate two independent random walks of 1,000 observations,
calling them Walk1 and Walk2. Fit the bivariate linear model that relates Walk1 to
Walk2 and report your regression results.
b. Recall the Monte Carlo simulation exercise in HW 4, Question 3c. Using a similar
approach, repeat a. above 1,000 times, each time recording the estimated value of the
slope coefficient of the bivariate regression. Generate a histogram of your 1,000
replications. How do these results compare to those you found in HW 4, Question 3c?
c. Consider your results in 2b as well as the dispersion in your histogram. Is there
something about independent unit roots that may lead one to find correlation when
there is none?
d. Submit code and results.
