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H6
HW3 (due Jan. 31).
Exercise 4.4 from the textbook and
Problem 1
Explore the correlation structure of the following models,
12
.7
.5
,
.7
.3
,
tt
t
t
t
t
X
XX
XZ
Z
Z
−−
=−+
=+
−
Z
by simulating their realizatins of 500 observations and computing ACFs and PACFs.
Comment on how these cut off.
Problem 2
Sample mean
100
0.157
X
=
was computed from a sample of size
100
generated from a MA(1)
process with mean
μ
and
2
0.6,
1
θσ
=
−=
.
Construct an approximate 95% CI for
.
Are the data compatible with the hypothesis that
0
=
?
_________________________________________________________________________________________________________
Confidence Intervals (CIs) for the Mean of a Stationary Time Series
is estimated from data by the
sample mean
1
1
n
nn
t
X
X
n
=
=
∑
.
For ARMA models,
v
~N
,
X
n
⎛⎞
⎜⎟
⎝⎠
&
,
where for large
,
n
v(
h
h
)
γ
∞
=−∞
=
∑
,
or
()
,
2
X
hh
γσ
ρ
=
2
V
,
X
X
n
σ
⎜
⎜
&
⎟
⎟
,
where for large
,
.
n
1
V12
(
)
h
h
∞
=
∑
Then an approximate
100(1
)%
α
−
(or
1
−
)) CI for
is given by
1/
2
2
VV
,
X
X
Xz
αα
σσ
−+
,
where
is the
2
z
−
−
2
quantile of the standard normal distribution.
Example 1
An approximate 95% CI (or 0.95 CI) for
is given by
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.
 Spring '09
 gUR
 Correlation

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