The McGraw-Hill Series Economics essentials of economics brue, McConnell, and Flynn Essentials of Economics

418
Part Two
Relaxing the Assumptions of the Classical Model
7
As we will also see in 
Part 5,
even though 
Y
and 
X
are nonstationary, it is possible to find 
u
to be
stationary. We will explore the implication of that later on.
8
If 
s
=
0, we obtain 
E
(
u
2
t
). Since 
E
(
u
t
)
=
0 by assumption, 
E
(
u
2
t
) will represent the variance of the
error term, which obviously is nonzero (why?).
guj75772_ch12.qxd 14/08/2008 10:40 AM Page 418

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Chapter 12
Autocorrelation: What Happens If the Error Terms Are Correlated?
419
any practical use. As a starting point, or first approximation, one can assume that the dis-
turbance, or error, terms are generated by the following mechanism.
u
t
=
ρ
u
t
−
1
+
ε
t
−
1
< ρ <
1
(12.2.1)
where 
ρ
(
=
rho) is known as the 
coefficient of autocovariance
and where 
ε
t
is the sto-
chastic disturbance term such that it satisfies the standard OLS assumptions, namely,
E
(
ε
t
)
=
0
var (
ε
t
)
=
σ
2
ε
(12.2.2)
cov (
ε
t
,
ε
t
+
s
)
=
0
s
=
0
In the engineering literature, an error term with the preceding properties is often called
a