<s>
In	O
statistics	O
,	O
an	O
augmented	B-General_Concept
Dickey	I-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
(	O
ADF	O
)	O
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
a	O
time	O
series	O
sample	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>
It	O
is	O
an	O
augmented	O
version	O
of	O
the	O
Dickey	B-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
for	O
a	O
larger	O
and	O
more	O
complicated	O
set	O
of	O
time	O
series	O
models	O
.	O
</s>
<s>
Consequently	O
,	O
there	O
are	O
three	O
main	O
versions	O
of	O
the	O
test	O
,	O
analogous	O
to	O
the	O
ones	O
discussed	O
on	O
Dickey	B-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
(	O
see	O
that	O
page	O
for	O
a	O
discussion	O
on	O
dealing	O
with	O
uncertainty	O
about	O
including	O
the	O
intercept	O
and	O
deterministic	O
time	O
trend	O
terms	O
in	O
the	O
test	O
equation	O
.	O
)	O
</s>
<s>
An	O
alternative	O
approach	O
is	O
to	O
examine	O
information	O
criteria	O
such	O
as	O
the	O
Akaike	O
information	O
criterion	O
,	O
Bayesian	B-General_Concept
information	I-General_Concept
criterion	I-General_Concept
or	O
the	O
Hannan	B-General_Concept
–	I-General_Concept
Quinn	I-General_Concept
information	I-General_Concept
criterion	I-General_Concept
.	O
</s>
<s>
is	O
computed	O
it	O
can	O
be	O
compared	O
to	O
the	O
relevant	O
critical	O
value	O
for	O
the	O
Dickey	B-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
If	O
the	O
calculated	O
test	O
statistic	O
is	O
less	O
(	O
more	O
negative	O
)	O
than	O
the	O
critical	O
value	O
,	O
then	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
is	O
rejected	O
and	O
no	O
unit	O
root	O
is	O
present	O
.	O
</s>
<s>
In	O
this	O
case	O
the	O
and	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
not	O
rejected	O
.	O
</s>
<s>
In	O
contrast	O
,	O
when	O
the	O
process	O
has	O
no	O
unit	O
root	O
,	O
it	O
is	O
stationary	O
and	O
hence	O
exhibits	O
reversion	O
to	O
the	O
mean	O
-	O
so	O
the	O
lagged	O
level	O
will	O
provide	O
relevant	O
information	O
in	O
predicting	O
the	O
change	O
of	O
the	O
series	O
and	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
a	O
unit	O
root	O
will	O
be	O
rejected	O
.	O
</s>
<s>
This	O
is	O
more	O
negative	O
than	O
the	O
tabulated	O
critical	O
value	O
of	O
−	O
3.50	O
,	O
so	O
at	O
the	O
95	O
percent	O
level	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
a	O
unit	O
root	O
will	O
be	O
rejected	O
.	O
</s>
<s>
There	O
are	O
alternative	O
unit	B-General_Concept
root	I-General_Concept
tests	I-General_Concept
such	O
as	O
the	O
Phillips	B-General_Concept
–	I-General_Concept
Perron	I-General_Concept
test	I-General_Concept
(	O
PP	O
)	O
or	O
the	O
ADF-GLS	B-General_Concept
test	I-General_Concept
procedure	O
(	O
ERS	O
)	O
developed	O
by	O
Elliott	O
,	O
Rothenberg	O
and	O
Stock	O
(	O
1996	O
)	O
.	O
</s>
<s>
In	O
R	B-Language
,	O
there	O
are	O
various	O
packages	O
supplying	O
implementations	O
of	O
the	O
test	O
.	O
</s>
<s>
The	O
forecast	O
package	O
includes	O
a	O
ndiffs	O
function	O
(	O
which	O
handles	O
multiple	O
popular	O
unit	B-General_Concept
root	I-General_Concept
tests	I-General_Concept
)	O
,	O
the	O
tseries	O
package	O
includes	O
an	O
adf.test	O
function	O
and	O
the	O
fUnitRoots	O
package	O
includes	O
an	O
adfTest	O
function	O
.	O
</s>
<s>
Gretl	B-Application
includes	O
the	O
Augmented	B-General_Concept
Dickey	I-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
In	O
SAS	B-Language
,	O
PROC	O
ARIMA	O
can	O
perform	O
ADF	B-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
In	O
Stata	B-Algorithm
,	O
the	O
dfuller	O
command	O
is	O
used	O
for	O
ADF	B-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
In	O
EViews	B-Algorithm
,	O
the	O
Augmented	O
Dickey-Fuller	B-General_Concept
is	O
available	O
under	O
"	O
Unit	O
Root	O
Test.	O
"	O
</s>
<s>
In	O
Python	B-Language
,	O
the	O
adfuller	O
function	O
is	O
available	O
in	O
the	O
Statsmodels	B-Application
package	O
and	O
the	O
ARCH	O
package	O
also	O
provides	O
an	O
Augmented	B-General_Concept
Dickey	I-General_Concept
–	I-General_Concept
Fuller	I-General_Concept
test	I-General_Concept
.	O
</s>
<s>
In	O
Java	B-Language
,	O
the	O
AugmentedDickeyFuller	O
class	O
is	O
included	O
in	O
SuanShu	O
available	O
under	O
the	O
com.numericalmethod.suanshu.stats.test.timeseries.adf	O
package	O
.	O
</s>
<s>
In	O
Julia	B-Application
,	O
the	O
ADFTest	O
function	O
is	O
available	O
in	O
the	O
HypothesisTests	O
package	O
.	O
</s>
