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ORIE 4630 — D. Ruppert
Homework #3 — due Friday, Sep 17, 2010
1. Suppose that the log returns
r
1
,r
2
,r
3
,...
are iid
N
(0
.
001
,
0
.
06). (We use the notation
that the second parameter in a normal distribution, here 0.06, is the variance. This
is common notation, but not universal. For example, in
R
functions such as
pnorm
,
the second parameter is the standard deviation.) Let
r
4
(3) =
r
2
+
r
3
+
r
4
and
r
4
(4) =
r
1
+
r
2
+
r
3
+
r
4
be the 3period and 4period log returns at time 4.
(a) What is the covariance between
r
4
(3) and
r
4
(4)? (Hint: If you are having trouble
getting started, review the material in Section 2.17.1.)
(b) What is the conditional distribution of
r
4
(4) given that
r
4
(3) = 0
.
1?
2. In this problem you will ﬁt a
t
distribution by maximum likelihood to the daily log
returns for Siemens. The data are in the data set
siemens
that is part of the
evir
package. Run the following code:
library(evir)
library(fGarch)
data(siemens)
start_siemens = c(mean(siemens),sd(siemens),4)
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 '10
 RUPPERT

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