<s>
In	O
statistics	O
,	O
a	O
unit	B-General_Concept
root	I-General_Concept
test	I-General_Concept
tests	O
whether	O
a	O
time	O
series	O
variable	O
is	O
non-stationary	B-Algorithm
and	O
possesses	O
a	O
unit	B-Algorithm
root	I-Algorithm
.	O
</s>
<s>
The	O
null	O
hypothesis	O
is	O
generally	O
defined	O
as	O
the	O
presence	O
of	O
a	O
unit	B-Algorithm
root	I-Algorithm
and	O
the	O
alternative	O
hypothesis	O
is	O
either	O
stationarity	B-Algorithm
,	O
trend	O
stationarity	B-Algorithm
or	O
explosive	O
root	O
depending	O
on	O
the	O
test	O
used	O
.	O
</s>
<s>
In	O
general	O
,	O
the	O
approach	O
to	O
unit	B-Algorithm
root	I-Algorithm
testing	O
implicitly	O
assumes	O
that	O
the	O
time	O
series	O
to	O
be	O
tested	O
can	O
be	O
written	O
as	O
,	O
</s>
<s>
The	O
task	O
of	O
the	O
test	O
is	O
to	O
determine	O
whether	O
the	O
stochastic	O
component	O
contains	O
a	O
unit	B-Algorithm
root	I-Algorithm
or	O
is	O
stationary	O
.	O
</s>
<s>
here	O
the	O
null	O
hypothesis	O
is	O
trend	O
stationarity	B-Algorithm
rather	O
than	O
the	O
presence	O
of	O
a	O
unit	B-Algorithm
root	I-Algorithm
.	O
</s>
<s>
Unit	B-General_Concept
root	I-General_Concept
tests	I-General_Concept
are	O
closely	O
linked	O
to	O
serial	O
correlation	O
tests	O
.	O
</s>
<s>
However	O
,	O
while	O
all	O
processes	O
with	O
a	O
unit	B-Algorithm
root	I-Algorithm
will	O
exhibit	O
serial	O
correlation	O
,	O
not	O
all	O
serially	O
correlated	O
time	O
series	O
will	O
have	O
a	O
unit	B-Algorithm
root	I-Algorithm
.	O
</s>
