•
1.2. (0.5 point) You want to estimate the true kurtosis
θ
of
F
, which is unknown. Give a point estimate
of
θ
by computing the sample kurtosis of the
n
= 1257
daily log returns.
•
1.3. (0.5 point) A point estimate is not enough. You want to construct a confidence interval for
θ
.
You need to learn more about the sample kurtosis
T
=
g
(
X
1
,
· · ·
, X
n
) =
1
n
QQQQQQQ
n
i
=1
(
X
i
−
¯
X
n
)
4
(
1
n
QQQQQQQ
n
i
=1
(
X
i
−
¯
X
n
)
2
)
2
,
n
= 1257
.
As a function of a random sample
{
X
1
,
· · ·
, X
n
}
from
F
,
T
is random. What you computed in 1.2 is
only a numeric realization of
T
. You want to find out the sampling distribution of
T
. This sampling
distribution is unknown, but can be estimated using resampling. Use resampling to simulate
B
= 5000
values of the sample kurtosis from the empirical cdf
ˆ
F
. Construct a histogram of the sample kurtoses
(use 30 bins).
2
