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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?

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