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STAT 420
Fall 2007
Homework #13
(10 points)
(due Friday, December 7, by 3:00 p.m.)
1.
Given the time series
64
55
41
59
48
71
35
57
40
58
calculate
r
1
and
r
2
.
(
Note: In practice reliable autocorrelation estimates are only obtained from
series consisting of approximately 50 observations or more.
)
2.
The model
(
Y
t
–
μ
) =
φ
(
Y
t
– 1
–
μ
) +
e
t
has been fitted to a time series
giving
ˆ
=
0.6,
ˆ =
5.0, and
σ
ˆ
e
2
=
2.25. The last five values of the series
are
5.5, 4.8, 4.5, 5.6, 4.7. Using the time of the last observation as the
forecast origin, calculate the forecasts and approximate 95% probability limits
for the next
three
observations.
3.
Suppose that
N
observations from the AR(2) model gave the following sample ACF:
r
1
=
1
ˆ
= 0.8,
r
2
=
2
ˆ
= 0.5. Use the YuleWalker equations to estimate
1
and
2
.
4.
Consider the ARMA
(
1, 1
) model
(
Y
t
– 60
) + 0.3 (
Y
t
– 1
– 60
) =
e
t
– 0.4
e
t
– 1
which was fitted to a time series where the last 10 values are
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This note was uploaded on 04/29/2010 for the course STAT stat 420 taught by Professor Stepanov during the Spring '07 term at University of Illinois at Urbana–Champaign.
 Spring '07
 STEPANOV
 Correlation

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