<s>
Symmetric	B-General_Concept
mean	I-General_Concept
absolute	I-General_Concept
percentage	I-General_Concept
error	I-General_Concept
(	O
SMAPE	B-General_Concept
or	O
sMAPE	B-General_Concept
)	O
is	O
an	O
accuracy	O
measure	O
based	O
on	O
percentage	O
(	O
or	O
relative	O
)	O
errors	O
.	O
</s>
<s>
The	O
earliest	O
reference	O
to	O
similar	O
formula	O
appears	O
to	O
be	O
Armstrong	O
(	O
1985	O
,	O
p.348	O
)	O
where	O
it	O
is	O
called	O
"	O
adjusted	O
MAPE	B-General_Concept
"	O
and	O
is	O
defined	O
without	O
the	O
absolute	O
values	O
in	O
denominator	O
.	O
</s>
<s>
Therefore	O
the	O
currently	O
accepted	O
version	O
of	O
SMAPE	B-General_Concept
assumes	O
the	O
absolute	O
values	O
in	O
the	O
denominator	O
.	O
</s>
<s>
In	O
contrast	O
to	O
the	O
mean	B-General_Concept
absolute	I-General_Concept
percentage	I-General_Concept
error	I-General_Concept
,	O
SMAPE	B-General_Concept
has	O
both	O
a	O
lower	O
bound	O
and	O
an	O
upper	O
bound	O
.	O
</s>
<s>
One	O
supposed	O
problem	O
with	O
SMAPE	B-General_Concept
is	O
that	O
it	O
is	O
not	O
symmetric	O
since	O
over	O
-	O
and	O
under-forecasts	O
are	O
not	O
treated	O
equally	O
.	O
</s>
<s>
This	O
is	O
illustrated	O
by	O
the	O
following	O
example	O
by	O
applying	O
the	O
second	O
SMAPE	B-General_Concept
formula	O
:	O
</s>
<s>
Under-forecasting	O
:	O
At	O
=	O
100	O
and	O
Ft	O
=	O
90	O
give	O
SMAPE	B-General_Concept
=	O
5.26	O
%	O
.	O
</s>
<s>
However	O
,	O
one	O
should	O
only	O
expect	O
this	O
type	O
of	O
symmetry	O
for	O
measures	O
which	O
are	O
entirely	O
difference-based	O
and	O
not	O
relative	O
(	O
such	O
as	O
mean	B-Algorithm
squared	I-Algorithm
error	I-Algorithm
and	O
mean	O
absolute	O
deviation	O
)	O
.	O
</s>
<s>
There	O
is	O
a	O
third	O
version	O
of	O
SMAPE	B-General_Concept
,	O
which	O
allows	O
to	O
measure	O
the	O
direction	O
of	O
the	O
bias	O
in	O
the	O
data	O
by	O
generating	O
a	O
positive	O
and	O
a	O
negative	O
error	O
on	O
line	O
item	O
level	O
.	O
</s>
<s>
A	O
limitation	O
to	O
SMAPE	B-General_Concept
is	O
that	O
if	O
the	O
actual	O
value	O
or	O
forecast	O
value	O
is	O
0	O
,	O
the	O
value	O
of	O
error	O
will	O
boom	O
up	O
to	O
the	O
upper-limit	O
of	O
error	O
.	O
</s>
