Fundamentals of Business Analytics
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BUSN 5502 Fundamentals of Business Analytics Final Exam Preliminaries - Fundamentals of Business Analytics - ECON5002
2. Two R-code scripts - label the files as q.r by
16:40 pm.
I should be able to run your script file and reproduce the results that you will report
in the exam.
1. The data capm v0.csv have observations from daily rates of return comprising the
period of January 2007 to December 2013. The variables are described below:
data capm v0.csv
Date day/month/year
Mkt.RF Market minus Risk free return
SMB Return of companies with low market capitalization
HML Return of companies with high book-to-market values
RF Risk Free return
GE General Electric
CISCO CISCO
DD DuPont
XOM Exxon-Mobil
DJI Down Jones Insdustrial Average
AXP American Express Company
MMM 3M Company
ATT AT&T Inc.
BA Boing Company
CAT Caterpillar Inc.
Let us explore again the CAPM model. The regression models to be investigated include
r[?] − rrf = α + β × (rmkt − rrf ) + u.
r[?] − rrf = α + β × (rmkt − rrf ) + γ × smb+ u
r[?] − rrf = α + β × (rmkt − rrf ) + δ × hml + u..
r[?] − rrf = α + β × (rmkt − rrf ) + γ × smb+ δ × hml + u.
where r[?] is the return of one asset to be informed on the exam paper, rrf is the risk free
return, rmkt is the market return, and smb and hml correspond to SMB and HTM defined
in the above Table. The variable u is the error term. You should be able to:
1
BUSN 5502 Fundamentals of Business Analytics
1. (a) Obtain a summary statistics of each of the return series.
(b) Produce a scatter plot with (r[?]−rrf ) on the y-axis and (rmkt − rrf ) on the x-axis,
and include the regression line in it.
(c) Estimate α, β, γ, and δ and their respective standard errors. Verify if the es-
timated coefficients are statistically significant. Interpret the coefficients of the
regressions.
(d) Estimate confidence intervals for α, β, γ, and δ possibly assuming heteroskedas-
ticity of the variance of the residuals.
(e) Perform hypothesis testing on the parameters of the model (single or joint rescric-
tions) possibly assuming heteroskedasticity of the variance of the errors.
(f) Test if the errors are heteroskedastic (Breustch-Pagan test), and interpret the
result.
(g) Perform model comparision tests, considering that one or more models are nested
into a large model (waldtest).
2. We now study the behavior of the inflation of finished goods derived from inflation
finished goods.csv data, which is quarterly data from 1960:2 to 2008:2 of the USA
economy (193 observations). Let us call this series yt which can follow an ARMA(p,q)
process
yt = µ+ φ1yt−1 + . . .+ φpyt−p + υt + ψ1υt−1 + . . .+ ψqυt−q
The lags of the autoregressive and moving average components will be informed on the
exam. You should be able to:
(a) Plot the series across time.
(b) Plot the autocorrelation and partial autocorrelation functions, and use this infor-
mation to determine the order of the ARMA.
(c) Estimate µ, φ′s, and ψ′s, and their respective standard errors. Verify if the
estimated coefficients are statistically significant.
(d) Perform diagnostic tests (Ljung-Box).
(e) Perform model comparision (AIC and BIC).