Time Series: Data sequentially collected over time.
AR(1): X
i
= λX
i1
+Y
i
.
The Y
i
’s are from a uniform [1, 1] distribution and λ is a constant.
For this AR(1) process, X
1
= λX
0
+Y
1
,
X
49
0
0
∑
=
=
i
i
i
Y
λ
and the Yi's are from a uniform [1,
1] distribution. By the use of the Central Limit Theorem, the X
0
's are approximately
normally distributed with a mean of 0 and a variance of
)
1
(
3
1
2
100


.
Use three different values
of lambda: λ = 0.5, λ = 0.35 and λ = 0.5
Measure of accuracy: The Average Relative Error formula is used as a measure of
accuracy:


200
1
ARE
200
1
,
n
∑
=
=

i
i
n
n
n
B
V
V
, where V
n
is the sample variance of the Monte
Carlo 1000 sample medians of sample size n and B
n,i
is the bootstrap sample variance of
the bootstrap sample medians. 200 is the number of bootstrap subsamples. The details
NonOverlapping Moving Block Bootstrap, aka: Disjoint Block Bootstrap.
11
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 Spring '09
 qian
 Statistics, Normal Distribution, Variance, Moving Block Bootstrapping

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