<s>
In	O
statistics	O
,	O
the	O
Dickey	B-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
tests	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
that	O
a	O
unit	O
root	O
is	O
present	O
in	O
an	O
autoregressive	B-Algorithm
(	O
AR	B-Algorithm
)	O
time	O
series	O
model	O
.	O
</s>
<s>
The	O
alternative	B-General_Concept
hypothesis	I-General_Concept
is	O
different	O
depending	O
on	O
which	O
version	O
of	O
the	O
test	O
is	O
used	O
,	O
but	O
is	O
usually	O
stationarity	B-Algorithm
or	O
trend-stationarity	O
.	O
</s>
<s>
The	O
model	O
would	O
be	O
non-stationary	B-Algorithm
in	O
this	O
case	O
.	O
</s>
<s>
where	O
is	O
the	O
first	B-Algorithm
difference	I-Algorithm
operator	I-Algorithm
and	O
.	O
</s>
<s>
In	O
each	O
case	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
that	O
there	O
is	O
a	O
unit	O
root	O
,	O
.	O
</s>
<s>
The	O
tests	O
have	O
low	O
statistical	B-General_Concept
power	I-General_Concept
in	O
that	O
they	O
often	O
cannot	O
distinguish	O
between	O
true	O
unit-root	O
processes	O
(	O
)	O
and	O
near	O
unit-root	O
processes	O
(	O
is	O
close	O
to	O
zero	O
)	O
.	O
</s>
<s>
If	O
the	O
series	O
is	O
stationary	B-Algorithm
(	O
or	O
trend-stationary	O
)	O
,	O
then	O
it	O
has	O
a	O
tendency	O
to	O
return	O
to	O
a	O
constant	O
(	O
or	O
deterministically	O
trending	O
)	O
mean	O
.	O
</s>
<s>
There	O
is	O
also	O
an	O
extension	O
of	O
the	O
Dickey	O
–	O
Fuller	O
(	O
DF	O
)	O
test	O
called	O
the	O
augmented	B-General_Concept
Dickey	I-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
(	O
ADF	O
)	O
,	O
which	O
removes	O
all	O
the	O
structural	O
effects	O
(	O
autocorrelation	O
)	O
in	O
the	O
time	O
series	O
and	O
then	O
tests	O
using	O
the	O
same	O
procedure	O
.	O
</s>
<s>
The	O
decision	O
is	O
important	O
for	O
the	O
size	O
of	O
the	O
unit	O
root	O
test	O
(	O
the	O
probability	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
a	O
unit	O
root	O
when	O
there	O
is	O
one	O
)	O
and	O
the	O
power	O
of	O
the	O
unit	O
root	O
test	O
(	O
the	O
probability	O
of	O
rejecting	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
a	O
unit	O
root	O
when	O
there	O
is	O
not	O
one	O
)	O
.	O
</s>
<s>
Elder	O
and	O
Kennedy	O
(	O
2001	O
)	O
present	O
a	O
simple	O
testing	O
strategy	O
that	O
avoids	O
double	O
and	O
triple	O
testing	O
for	O
the	O
unit	O
root	O
that	O
can	O
occur	O
with	O
other	O
testing	O
strategies	O
,	O
and	O
discuss	O
how	O
to	O
use	O
prior	O
knowledge	O
about	O
the	O
existence	O
or	O
not	O
of	O
long-run	O
growth	O
(	O
or	O
shrinkage	O
)	O
in	O
y	O
.	O
Hacker	O
and	O
Hatemi-J	O
(	O
2010	O
)	O
provide	O
simulation	B-Application
results	O
on	O
these	O
matters	O
,	O
including	O
simulations	O
covering	O
the	O
Enders	O
(	O
2004	O
)	O
and	O
Elder	O
and	O
Kennedy	O
(	O
2001	O
)	O
unit-root	O
testing	O
strategies	O
.	O
</s>
<s>
Simulation	B-Application
results	O
are	O
presented	O
in	O
Hacker	O
(	O
2010	O
)	O
which	O
indicate	O
that	O
using	O
an	O
information	B-General_Concept
criterion	I-General_Concept
such	O
as	O
the	O
Schwarz	B-General_Concept
information	I-General_Concept
criterion	I-General_Concept
may	O
be	O
useful	O
in	O
determining	O
unit	O
root	O
and	O
trend	O
status	O
within	O
a	O
Dickey	O
–	O
Fuller	O
framework	O
.	O
</s>
