McMaster University
DeGroote School of Business
Introduction to Econometrics, MFIN 701
Assignment 2
Due March 13, 2022
Hand in a copy of your computer output and a separate write-up of the answers
to Avenue Assignment 2 to the following questions. Writing answers
on your computer output is not acceptable. Each student’s write-up
should be done independently.
This assignment will explore prediction of monthly returns given various
predictor variables. The dataset is gw2020-n.dat and the column CRSP SPvw
we will use as monthly returns rt
. The remaining columns (except CRSP SPvwx)
list regressors available at time t. Scale all data by 12 to put it into annual
terms.
1. Consider the following model to predict rt
rt = Xt−1β + t
, t ∼ iid(0, σ2
), (1)
where Xt−1 consists of the regressors: tbl,lty,Rfree,infl,ltr,svar along
with rt−1. Note the lag t − 1 on the regressors. Answer the following
questions.
(a) Estimate the model by OLS and report estimates. To what extent
are monthly returns predictable by these regressors? What
regressors are significant?
(b) Test for autocorrelation using a Breusch-Godfrey test with one
lag. What are your conclusions? Test for heteroskedasticity using
a Breush-Pagan statistic. What are your conclusions?
(c) If heteroskedasticity is present re-estimate the model with robust
standard errors. Does the significance of any regressors change?
(d) Use an F-test to remove any insignificant regressors. What is your
final model? (Always include at least an intercept in the model).
(e) Using an AR(1) model for returns perform a structural break test
on the conditional mean parameters (intercept and coefficient on
rt−1) for the financial crisis period 2007-2009. Is there any evidence
of a structural break?
2. Consider the following AR(1)-ARCH(2) model,
(a) What parameter restrictions are sufficient for positive conditional
variances? What is the value of E[σ2t] and why is this different
than the conditional variance σ2t?
(b) Estimate the model by maximum likelihood and report standard
errors and t-tests for parameters. See mle arch.r for an example.
Is there heteroskedasticity in the error terms? Provide a time
series plot of σ
t using your estimates.
(c) Estimate a GARCH(1,1) model. Is this better than the ARCH(2)
above? Is it possible to perform a likelihood ratio test to decide
between these models?