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Homework (cointegration)
1.
What does Y
t
~ I(d) mean?
2.
Let
Y
t
(Y
1t
, Y
2t
)’. What does “
Y
t
~ CI(d,b)” mean?
3.
Explain how the cointegration concept could be used to study economic equilibrium
relationships. Use an economic example to illustrate your argument.
4.
Consider the bivariate system Y
1t
=
Y
2t
+
1t
and Y
2t
= Y
2t1
+
2t
, where
1t
=
1t
+ k
1
,
2t
=
2t
+ k
2
, k
1
and k
2
are constants, and
1t
and
2t
are independent white noises.
a.
Show that
∆
Y
t
= (1  L)
1
t
2
t
=
1
L
01
k
1
k
2
+
1
L
0
1
1
t
2
t
b.
Show that E(
∆
Y
t
) =
1
2
1
L
0
1
k
1
k
2
and the cointegrating vector is
orthogonal to E(
∆
Y
t
).
c.
Show
∆
Y
t
=
1
2
+
1
L
0
1
1
t
2
t
, where
u
1
u
2
is defined in (b).
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This note was uploaded on 09/29/2010 for the course ECON Econometri taught by Professor Fairlie during the Winter '09 term at University of California, Santa Cruz.
 Winter '09
 Fairlie

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