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The homework has to be stapled.
PSTAT 174/274. Homework #2
Name:
Due:
10/23/06 at the beginning of the discussion session
Score:
/10
Credit:
People you worked with:
Sources consulted(Reference):
1. (2 points) For an MA(1),
x
t
=
w
t
+
θw
t

1
, show that

ρ
x
(1)
 ≤
1
/
2 for any number
θ
. For which
values of
θ
does
ρ
x
(1) attain its maximum and minimum?
2. (1 point each) Identify the following models as ARMA(
p,q
) models (watch out for parameter re
dundancy), and determine whether they are causal and/or invertible:
(a)
x
t
= 0
.
80
x
t

1
±
0
.
15
x
t

2
+
w
t
±
0
.
30
w
t

1
(b)
x
t
=
x
t

1
±
0
.
50
x
t

2
+
w
t
±
w
t

1
3. (2 points) For the AR(2) model given by
x
t
=
±
0
.
9
x
t

2
+
w
t
, ﬁnd the roots of the autoregressive
polynomial and then sketch the ACF,
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This note was uploaded on 05/01/2009 for the course PSTAT 120A taught by Professor Mackgalloway during the Spring '08 term at UCSB.
 Spring '08
 MACKGALLOWAY

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