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ORIE 4630 — D. Ruppert
Homework #13 — Friday, Dec 3, 2010
Note:
Students are required to work independently on homework.
1. The problem uses the same data set that was used in the lectures this week. You can
obtain the data with the following
R
code.
options(digits=4)
library("Ecdat")
data(Capm)
r = Capm$rf
n = length(r)
lagr = r[1:(n1)]
diffr = r[2:n]  lagr
Fit the model
∆(
r
t
) =
β
(
r
t

1

α
) +
θ
1
/
2
(
r
t

1
)
γ/
2
ϵ
t
by estimating (
α, β, θ, γ
) simultaneously by maximum likelihood. Assume that
ϵ
1
, . . . , ϵ
n
are independent
N
(0
,
1). Find standard errors for all four parameters using the Fisher
information matrix. Include your
R
program with your homework.
2. This problem uses monthly observations of the 2month yield, i.e.,
Y
T
with
T
equal to
2 months. The rates were logtransformed to stabilize the variance. To ﬁt a GARCH
model to the changes in the logrates, the following
R
code was run:
library(fGarch)
library(Ecdat)
data(Irates)
r = as.numeric(log(Irates[,2]))
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 RUPPERT

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