<s>
Surrogate	B-General_Concept
data	I-General_Concept
testing	I-General_Concept
(	O
or	O
the	O
method	O
of	O
surrogate	O
data	O
)	O
is	O
a	O
statistical	O
proof	O
by	O
contradiction	O
technique	O
and	O
similar	O
to	O
permutation	B-General_Concept
tests	I-General_Concept
and	O
as	O
a	O
resampling	B-General_Concept
technique	O
related	O
(	O
but	O
different	O
)	O
to	O
parametric	B-Application
bootstrapping	I-Application
.	O
</s>
<s>
The	O
technique	O
basically	O
involves	O
specifying	O
a	O
null	B-General_Concept
hypothesis	I-General_Concept
describing	O
a	O
linear	B-Algorithm
process	I-Algorithm
and	O
then	O
generating	O
several	O
surrogate	O
data	O
sets	O
according	O
to	O
using	O
Monte	B-Algorithm
Carlo	I-Algorithm
methods	I-Algorithm
.	O
</s>
<s>
If	O
the	O
value	O
of	O
the	O
statistic	O
is	O
significantly	O
different	O
for	O
the	O
original	O
series	O
than	O
for	O
the	O
surrogate	O
set	O
,	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
is	O
rejected	O
and	O
non-linearity	O
assumed	O
.	O
</s>
<s>
The	O
particular	O
surrogate	B-General_Concept
data	I-General_Concept
testing	I-General_Concept
method	O
to	O
be	O
used	O
is	O
directly	O
related	O
to	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
This	O
concept	O
is	O
also	O
used	O
in	O
permutation	B-General_Concept
tests	I-General_Concept
.	O
</s>
<s>
This	O
method	O
is	O
associated	O
to	O
the	O
null	B-General_Concept
hypothesis	I-General_Concept
of	O
the	O
data	O
being	O
uncorrelated	O
i.i.d	O
noise	O
(	O
possibly	O
Gaussian	O
and	O
measured	O
by	O
a	O
static	O
nonlinear	O
function	O
)	O
.	O
</s>
<s>
Algorithm	O
1	O
,	O
or	O
RP	O
(	O
for	O
Random	O
Phases	O
;	O
also	O
known	O
as	O
FT	O
,	O
for	O
Fourier	B-Algorithm
Transform	I-Algorithm
)	O
:	O
In	O
order	O
to	O
preserve	O
the	O
linear	O
correlation	O
(	O
the	O
periodogram	O
)	O
of	O
the	O
series	O
,	O
surrogate	O
data	O
are	O
created	O
by	O
the	O
inverse	O
Fourier	B-Algorithm
Transform	I-Algorithm
of	O
the	O
modules	O
of	O
Fourier	B-Algorithm
Transform	I-Algorithm
of	O
the	O
original	O
data	O
with	O
new	O
(	O
uniformly	O
random	O
)	O
phases	O
.	O
</s>
<s>
Algorithm	O
2	O
,	O
or	O
AAFT	O
(	O
for	O
Amplitude	O
Adjusted	O
Fourier	B-Algorithm
Transform	I-Algorithm
)	O
:	O
This	O
method	O
has	O
approximately	O
the	O
advantages	O
of	O
the	O
two	O
previous	O
ones	O
:	O
it	O
tries	O
to	O
preserve	O
both	O
the	O
linear	O
structure	O
and	O
the	O
amplitude	O
distribution	O
.	O
</s>
<s>
Iterative	O
algorithm	O
2	O
,	O
or	O
IAAFT	O
(	O
for	O
Iterative	O
Amplitude	O
Adjusted	O
Fourier	B-Algorithm
Transform	I-Algorithm
)	O
:	O
This	O
algorithm	O
is	O
an	O
iterative	O
version	O
of	O
AAFT	O
.	O
</s>
<s>
The	O
above	O
mentioned	O
techniques	O
are	O
called	O
linear	O
surrogate	O
methods	O
,	O
because	O
they	O
are	O
based	O
on	O
a	O
linear	B-Algorithm
process	I-Algorithm
and	O
address	O
a	O
linear	O
null	B-General_Concept
hypothesis	I-General_Concept
.	O
</s>
<s>
Time	O
series	O
exhibiting	O
strong	O
periodicities	O
are	O
clearly	O
not	O
consistent	O
with	O
the	O
linear	O
null	B-General_Concept
hypotheses	I-General_Concept
.	O
</s>
<s>
To	O
tackle	O
this	O
case	O
,	O
some	O
algorithms	O
and	O
null	B-General_Concept
hypotheses	I-General_Concept
have	O
been	O
proposed	O
.	O
</s>
