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F
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c
a
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f
p
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f
f
in
a
n
c
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e
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o
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h
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m
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f
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ti
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m
s
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n
d
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s
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8938
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eq
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ex
tr
ac
t
tr
en
d
s
an
d
p
atter
n
s
in
a
g
iv
e
n
d
ata
s
et.
T
r
ain
ed
A
NNs
ca
n
b
e
co
n
s
id
er
ed
as
ex
p
er
t
s
y
s
te
m
s
in
th
eir
d
o
m
ain
[
2
]
.
Ho
w
e
v
er
,
w
it
h
in
v
ar
io
u
s
ANNs,
c
h
o
o
s
in
g
th
e
b
est
o
n
e
f
o
r
a
g
i
v
en
p
r
o
b
lem
is
a
v
er
y
i
m
p
o
r
tan
t
tas
k
[
3
]
.
T
h
e
b
est
ch
o
ice
is
n
atu
r
all
y
th
e
o
n
e
g
i
v
in
g
m
o
s
t
e
f
f
icie
n
t
f
o
r
ec
ast f
o
r
th
e
p
r
o
b
le
m
at
h
a
n
d
.
A
lar
g
e
a
m
o
u
n
t
o
f
w
o
r
k
h
as
b
ee
n
d
o
n
e
b
y
r
esear
c
h
er
s
d
e
m
o
n
s
tr
atin
g
t
h
e
f
o
r
ec
asti
n
g
p
o
w
er
o
f
A
I
/
A
N
N
b
ased
m
et
h
o
d
s
in
v
ar
io
u
s
d
is
cip
lin
e
s
.
A
b
r
ief
r
ev
ie
w
o
f
it
i
s
g
i
v
en
h
er
e.
A
c
r
is
p
r
ev
ie
w
o
f
th
e
ef
f
icien
c
y
o
f
A
I
tec
h
n
iq
u
e
s
f
o
r
d
iag
n
o
s
t
ic
s
y
s
te
m
s
[
4
]
.
Var
io
u
s
A
NN
m
et
h
o
d
s
lik
e
GDM
,
C
o
n
j
u
g
ate
Gr
ad
ien
t,
Qu
as
i
Ne
w
to
n
a
n
d
L
M
m
eth
o
d
to
p
r
ed
ic
t
an
d
cla
s
s
i
f
y
t
h
e
p
atien
ts
w
it
h
h
ea
r
t
d
i
s
ea
s
e
[
5
]
.
E
m
p
lo
y
ed
a
b
ac
k
p
r
o
p
ag
atio
n
m
e
th
o
d
with
m
o
d
if
ied
lear
n
in
g
r
ate
a
n
d
m
o
m
e
n
t
u
m
f
ac
to
r
s
a
n
d
ap
p
lied
th
e
m
et
h
o
d
to
b
r
ea
s
t
ca
n
ce
r
an
d
ir
i
s
d
ata
s
ets
[
6
]
.
T
h
eir
s
tu
d
y
s
h
o
w
s
a
n
i
m
p
r
e
s
s
i
v
e
d
ec
r
ea
s
e
i
n
t
h
e
tr
ain
i
n
g
ti
m
es
o
f
b
ac
k
p
r
o
p
ag
atio
n
w
h
ic
h
i
s
o
th
er
w
i
s
e
in
h
er
en
tl
y
p
la
g
u
ed
b
y
s
lo
w
lear
n
i
n
g
an
d
lo
ca
l
m
i
n
i
m
a
p
r
o
b
le
m
s
.
A
f
ee
d
f
o
r
w
ar
d
A
NN
m
o
d
el
w
ith
th
e
ap
p
licatio
n
o
f
L
M
lear
n
i
n
g
a
lg
o
r
ith
m
f
o
r
s
h
o
r
t
-
ter
m
lo
ad
f
o
r
ec
asti
n
g
o
f
d
ail
y
p
ea
k
lo
ad
an
d
d
em
o
n
s
tr
ated
th
at
t
h
e
p
r
o
p
o
s
ed
A
NN
m
o
d
el
g
iv
e
s
m
o
r
e
ac
cu
r
ate
p
r
ed
ictio
n
s
w
it
h
o
p
ti
m
a
l
n
u
m
b
er
o
f
n
e
u
r
o
n
s
in
t
h
e
h
id
d
en
la
y
er
[
7
]
.
A
NN
an
d
R
an
d
o
m
Fo
r
est
(
R
F)
ap
p
r
o
ac
h
es
f
o
r
s
h
o
r
t
-
ter
m
p
h
o
to
v
o
ltaic
(
P
V)
o
u
tp
u
t
cu
r
r
en
t
f
o
r
ec
asti
n
g
(
ST
P
C
F)
f
o
r
th
e
n
ex
t
2
4
-
h
o
u
r
s
.
T
h
e
r
esu
l
ts
h
a
v
e
s
h
o
w
n
t
h
at
b
o
th
th
e
p
r
o
p
o
s
ed
tech
n
iq
u
es
ar
e
ab
le
to
p
er
f
o
r
m
f
o
r
ec
asti
n
g
o
f
f
u
tu
r
e
h
o
u
r
l
y
P
V
o
u
tp
u
t
cu
r
r
en
t
e
f
f
icie
n
tl
y
[
8
]
.
A
m
er
g
ed
L
o
n
g
S
h
o
r
t
-
ter
m
Me
m
o
r
y
(
L
ST
M)
f
o
r
f
o
r
ec
asti
n
g
g
r
o
u
n
d
v
i
s
ib
ilit
y
at
t
h
e
a
ir
p
o
r
t
b
y
co
m
b
i
n
i
n
g
ti
m
e
s
er
ies
o
f
p
r
ed
icto
r
v
ar
iab
le
w
it
h
an
o
t
h
er
m
o
d
er
ati
n
g
v
ar
iab
le.
Fo
r
ec
asti
n
g
ac
cu
r
ac
y
t
h
u
s
i
m
p
r
o
v
ed
o
v
er
t
h
e
tr
ad
itio
n
al
L
ST
M
m
e
th
o
d
[
9
]
.
A
NNs
to
d
iag
n
o
s
e
m
e
lan
o
m
a
s
k
i
n
ca
n
c
er
at
an
ea
r
l
y
s
ta
g
e
w
it
h
a
h
i
g
h
d
eg
r
ee
o
f
ac
cu
r
ac
y
[
1
0
]
.
A
p
p
lied
v
ar
io
u
s
n
eu
r
o
co
m
p
u
ti
n
g
m
et
h
o
d
s
f
o
r
r
ain
f
al
l
f
o
r
ec
asti
n
g
g
iv
i
n
g
h
ig
h
l
y
ac
c
u
r
ate
r
es
u
lt
s
[
1
1
]
.
P
r
o
p
o
s
ed
an
d
test
ed
a
n
e
w
h
y
b
r
id
m
o
d
el,
i.e
.
Gen
er
alize
d
Sp
ac
e
-
T
i
m
e
Au
to
r
eg
r
e
s
s
i
v
e
w
it
h
E
x
o
g
e
n
o
u
s
Var
iab
le
an
d
a
Ne
u
r
al
Net
w
o
r
k
(
GST
A
R
X
-
NN)
m
o
d
el
f
o
r
f
o
r
ec
asti
n
g
s
p
ac
e
-
ti
m
e
d
ata
w
i
th
ca
len
d
ar
v
ar
iati
o
n
ef
f
ec
t.
T
h
e
y
f
o
u
n
d
t
h
at
t
h
e
h
y
b
r
id
GST
AR
X
-
NN
m
o
d
el
g
av
e
m
o
r
e
ac
c
u
r
ate
f
o
r
ec
asts
th
a
n
t
h
e
tr
ad
itio
n
a
l
GST
AR
X
m
o
d
els
[
1
2
]
.
C
o
m
p
ar
ed
a
f
e
w
v
ar
ian
t
s
o
f
ex
p
o
n
e
n
tial
an
d
b
ac
k
p
r
o
p
ag
atio
n
A
NN
m
o
d
el
s
to
f
o
r
ec
ast
r
ice
p
r
o
d
u
ctio
n
.
T
h
e
r
esu
lts
s
h
o
w
ed
t
h
at
n
e
u
r
a
l
n
et
w
o
r
k
m
et
h
o
d
is
p
r
ef
er
ab
le
to
th
e
s
tatis
tical
m
eth
o
d
s
i
n
ce
it
r
esu
lts
in
lo
w
er
Me
an
Sq
u
ar
e
E
r
r
o
r
(
MSE
)
an
d
Me
an
A
b
s
o
lu
te
P
er
ce
n
tag
e
E
r
r
o
r
(
MA
P
E
)
[
1
3
]
.
A
I
h
as
a
ls
o
b
ee
n
u
s
ed
in
t
h
e
f
i
n
a
n
cial
s
ec
to
r
f
o
r
v
ar
io
u
s
k
in
d
s
o
f
f
o
r
ec
ast
s
,
an
al
y
s
es
a
n
d
d
ec
is
io
n
m
a
k
i
n
g
.
Used
o
f
m
ac
h
i
n
e
lear
n
i
n
g
al
g
o
r
ith
m
s
is
e
x
p
lo
r
ed
to
an
al
y
s
e
ef
f
ec
t
o
f
f
i
n
an
c
ial
n
e
w
s
o
n
s
to
ck
m
ar
k
et
p
r
ices
.
Su
p
p
o
r
t
Vec
to
r
Ma
ch
in
e
(
SVM)
an
d
R
F
al
g
o
r
ith
m
s
wer
e
u
s
ed
a
n
d
it
i
s
co
n
clu
d
ed
th
a
t
th
e
R
F
alg
o
r
it
h
m
g
i
v
e
s
b
etter
ac
cu
r
ac
y
in
c
o
m
p
ar
is
o
n
w
it
h
SVM
al
g
o
r
ith
m
[
1
4
]
.
P
r
o
p
o
s
ed
a
p
r
o
ce
d
u
r
e
to
c
o
n
s
tr
u
ct
T
r
ian
g
u
lar
F
u
zz
y
Nu
m
b
er
f
r
o
m
s
i
n
g
le
p
o
in
t
d
ata
an
d
th
e
n
u
s
e
d
an
Au
to
r
eg
r
es
s
iv
e
m
o
d
el
to
f
o
r
ec
ast
c
u
r
r
en
c
y
e
x
ch
a
n
g
e
r
ates
o
f
A
s
s
o
ciatio
n
o
f
So
u
t
h
E
ast
A
s
ian
Nat
io
n
(
ASE
A
N)
co
u
n
tr
ies
[
1
5
]
.
A
Fu
zz
y
Ne
u
r
al
S
y
s
te
m
(
FNS)
to
f
o
r
ec
ast
th
e
in
f
la
tio
n
r
ate
o
b
tain
in
g
b
etter
r
esu
lts
in
ter
m
s
o
f
R
MSE
th
an
tr
ad
itio
n
al
m
et
h
o
d
s
[
1
6
]
.
A
f
u
zz
y
s
et
s
m
et
h
o
d
p
r
ed
ictin
g
th
e
R
u
s
s
ia
T
r
ad
in
g
S
y
s
te
m
(
R
T
S)
in
d
ex
w
ith
a
co
n
f
id
e
n
ce
le
v
el
o
f
ab
o
u
t
9
0
%
t
h
o
u
g
h
h
a
v
i
n
g
o
n
l
y
an
i
n
c
o
m
p
lete
d
ata
s
et
at
h
a
n
d
[
1
7
]
.
A
h
y
b
r
id
m
o
d
el,
w
a
v
elet
r
ad
ial
b
ases
f
u
n
ctio
n
n
eu
r
al
n
e
t
w
o
r
k
s
(
W
R
B
FNN)
,
f
o
r
f
o
r
ec
asti
n
g
o
f
n
o
n
-
s
tatio
n
ar
y
ti
m
e
s
er
ie
s
a
n
d
f
o
u
n
d
t
h
at,
i
n
ter
m
s
o
f
M
A
P
E
an
d
M
SE,
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
s
u
p
er
io
r
to
t
h
e
tr
ad
iti
o
n
al
w
a
v
elet
f
ee
d
f
o
r
w
ar
d
n
e
u
r
al
n
et
w
o
r
k
s
(
W
F
FN)
m
o
d
el
[
1
8
]
.
I
n
th
e
p
r
esen
t
w
o
r
k
f
o
r
ec
ast
o
f
g
o
ld
p
r
ices
in
th
e
I
n
d
ia
n
M
u
lti
C
o
m
m
o
d
it
y
E
x
ch
a
n
g
e
m
ar
k
et,
M
C
X,
h
as
b
ee
n
tak
e
n
u
p
.
A
co
m
p
ar
ativ
e
an
al
y
s
i
s
o
f
g
o
ld
w
ith
o
th
er
in
v
e
s
t
m
en
t
o
p
tio
n
s
h
el
p
s
o
n
e
to
p
r
io
r
itize
ca
p
ital
in
v
e
s
t
m
e
n
ts
[
1
9
]
.
T
r
ad
itio
n
al
m
ath
e
m
at
ical
m
o
d
els
s
u
ch
a
s
Mo
v
i
n
g
a
v
er
ag
e
s
(
M
A)
,
A
u
to
-
R
e
g
r
es
s
i
v
e
Mo
v
in
g
Av
er
ag
e
s
(
A
R
M
A
)
,
Au
to
-
R
e
g
r
ess
i
v
e
I
n
teg
r
ated
M
o
v
in
g
Av
er
ag
e
s
(
A
R
I
M
A
)
etc.
as
w
ell
as
m
et
h
o
d
s
b
ased
o
n
A
I
s
u
c
h
as
t
h
e
A
N
N,
A
d
ap
tiv
e
Neu
r
o
F
u
zz
y
I
n
f
er
en
ce
S
y
s
te
m
s
(
A
N
FIS)
etc.
h
av
e
b
ee
n
d
ep
lo
y
e
d
b
y
m
an
y
r
esear
c
h
er
s
,
t
h
e
w
o
r
l
d
ar
o
u
n
d
,
f
o
r
g
o
ld
p
r
ice
f
o
r
ec
asti
n
g
ac
h
ie
v
i
n
g
v
ar
y
i
n
g
d
eg
r
ee
o
f
s
u
cc
e
s
s
.
Af
ter
m
ak
in
g
a
b
r
ief
r
ev
ie
w
o
f
th
e
s
e
r
esu
lts
w
e
p
r
ese
n
t o
u
r
w
o
r
k
o
n
g
o
ld
p
r
ice
f
o
r
ec
asti
n
g
.
I
n
o
u
r
w
o
r
k
w
e
h
a
v
e
p
r
o
p
o
s
ed
a
f
e
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I
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Vo
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9
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1
,
Ma
r
ch
20
20
:
46
–
57
48
A
N
N
alg
o
r
ith
m
s
,
ar
e
th
e
n
d
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lo
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ed
to
f
o
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ld
p
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in
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n
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ia.
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is
is
d
o
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b
y
s
y
s
te
m
atica
ll
y
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ep
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in
g
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th
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ab
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en
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ed
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et
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m
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ata
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d
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ican
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MP
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ter
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.
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cr
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ief
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o
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Sec
tio
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3
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s
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lts
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ed
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p
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t
w
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.
2.
RE
S
E
ARCH
M
E
T
H
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DO
L
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G
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A
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m
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a
rt
if
ic
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n
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w
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s
[2
0
]
.
It
m
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k
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s
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o
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[
2
1
]
.
T
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P
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f
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t
b
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k
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g
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n
[
2
2
]
.
S
o
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n
t
d
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ti
o
n
m
et
h
o
d
[
2
3
]
.
Q
u
as
i
N
e
w
to
n
m
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h
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d
m
a
y
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p
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ti
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T
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B
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tch
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a
n
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(
B
FGS)
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as
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th
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s
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Q
u
asi
Ne
w
to
n
m
et
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o
d
s
[
2
4
-
2
5
]
.
T
h
e
o
n
e
s
tep
s
ec
an
t
(
O
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)
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s
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m
u
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in
s
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ch
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w
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to
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m
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tech
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Qu
a
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p
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tat
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n
tag
e
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Hess
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m
a
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to
r
ag
e
at
ev
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y
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s
n
o
t
r
eq
u
ir
ed
[
2
6
]
.
T
h
e
L
M
m
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th
o
d
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er
p
o
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te
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G
a
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s
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-
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[
2
7
]
.
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[
2
8
]
.
B
a
y
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a
n
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q
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[
2
9
]
.
In
a
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c
h
o
s
e
n
f
o
r
t
h
e
p
r
e
s
en
t
s
t
u
d
y
.
V
ar
io
u
s
o
p
ti
m
i
z
at
i
o
n
fu
n
ct
io
n
s
ar
e
d
i
sc
u
s
se
d
i
n
n
e
x
t
se
ct
i
o
n
.
2
.
1
.
M
o
dified
G
DM
m
et
ho
d
s
I
n
th
e
p
r
esen
t
w
o
r
k
,
f
i
v
e
m
o
d
if
ied
GDM
m
eth
o
d
s
/al
g
o
r
it
h
m
s
h
av
e
b
ee
n
p
r
o
p
o
s
ed
an
d
d
ev
elo
p
ed
b
y
u
s
w
h
ic
h
i
n
co
r
p
o
r
ate
d
if
f
er
en
t
o
p
ti
m
izatio
n
f
u
n
ctio
n
s
i
n
s
te
ad
o
f
th
e
s
ta
n
d
ar
d
q
u
ad
r
atic
er
r
o
r
f
u
n
ctio
n
i
n
t
h
e
class
ical
GDM
to
f
o
r
ec
ast
t
h
e
g
o
ld
p
r
ice
[
3
0
-
3
1
]
.
T
h
ese
f
i
v
e
v
ar
ian
ts
o
f
t
h
e
o
p
ti
m
i
za
tio
n
f
u
n
ctio
n
ar
e
d
is
cu
s
s
ed
.
1.
Me
an
m
ed
ia
n
(
MM
D)
er
r
o
r
f
u
n
ctio
n
:
Me
a
n
Me
d
ia
n
er
r
o
r
f
u
n
ctio
n
i
s
g
iv
e
n
i
n
(
2
)
.
T
h
is
f
u
n
ctio
n
h
as
t
h
e
ad
v
an
ta
g
e
o
f
b
o
th
t
h
e
Me
a
n
e
r
r
o
r
f
u
n
ctio
n
an
d
Me
d
ian
er
r
o
r
f
u
n
ctio
n
.
I
t
r
ed
u
ce
s
th
e
i
n
f
l
u
en
ce
o
f
lar
g
e
er
r
o
r
s
.
=
∑
(
2
∗
(
√
1
+
(
2
2
⁄
)
)
−
1
)
(
2
)
2.
Min
k
o
w
s
k
i
(
MK
W
)
er
r
o
r
f
u
n
ctio
n
:
Mi
n
k
o
w
s
k
i
er
r
o
r
f
u
n
ctio
n
i
s
g
iv
e
n
in
(
3
)
.
MSE
er
r
o
r
ca
n
b
e
v
is
u
alize
d
as
a
s
p
ec
ial
ca
s
e
o
f
it
w
ith
r
=2
.
Var
iatio
n
s
o
f
r
ar
o
u
n
d
2
h
av
e
b
ee
n
o
b
s
e
r
v
ed
to
h
av
e
s
ig
n
i
f
ica
n
t in
f
l
u
e
n
ce
o
n
ac
cu
r
ac
y
o
f
f
o
r
ec
ast.
Her
e
r
h
a
s
b
ee
n
ch
o
s
e
n
to
b
e
0
.
4
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
r
ti
f
I
n
tell
I
SS
N:
2252
-
8938
A
N
N
b
a
s
ed
meth
o
d
fo
r
imp
r
o
vin
g
g
o
l
d
p
r
ice
fo
r
ec
a
s
tin
g
a
cc
u
r
a
cy
th
r
o
u
g
h
... (
S
h
ilp
a
V
erma
)
49
=
∑
|
|
(
3
)
3.
L
o
g
co
s
h
(
L
C
H)
er
r
o
r
f
u
n
ctio
n
:
L
o
g
co
s
h
er
r
o
r
f
u
n
c
tio
n
is
g
iv
e
n
i
n
(
4
)
.
I
t
ap
p
r
o
x
i
m
ate
s
x
2
/2
an
d
|
x
|
f
o
r
s
m
all
a
n
d
lar
g
e
v
al
u
es
o
f
x
r
esp
ec
tiv
el
y
.
=
∑
ln
(
c
osh
(
2
)
)
(
4
)
4.
C
au
c
h
y
(
C
C
Y)
er
r
o
r
f
u
n
ctio
n
:
C
au
c
h
y
er
r
o
r
f
u
n
ct
io
n
is
g
i
v
en
in
(
5
)
.
C
au
ch
y
er
r
o
r
f
u
n
ctio
n
is
k
n
o
w
n
to
s
h
o
w
r
o
b
u
s
t
n
ess
a
g
ain
s
t o
u
t
lier
s
.
=
∑
2
2
⁄
ln
(
1
+
(
)
2
)
ℎ
=
2
.
38
(
5
)
5.
Neg
ati
v
e
L
o
g
ar
it
h
m
ic
L
i
k
eli
h
o
o
d
(
NL
G)
er
r
o
r
f
u
n
ct
io
n
:
Neg
ati
v
e
L
o
g
ar
i
th
m
ic
L
ik
el
ih
o
o
d
er
r
o
r
f
u
n
ctio
n
i
s
g
iv
e
n
in
(
6
)
Neg
ativ
e
lo
g
ar
it
h
m
ic
lik
e
li
h
o
o
d
er
r
o
r
f
u
n
ctio
n
is
a
m
ea
s
u
r
e
o
f
ac
c
u
r
ac
y
o
f
a
class
i
f
ier
an
d
is
d
e
f
in
ed
as
f
o
ll
o
w
s
.
=
−
1
∑
ln
(
)
(
6
)
T
h
e
m
o
d
if
ied
al
g
o
r
ith
m
s
i
n
c
o
r
p
o
r
atin
g
th
e
ab
o
v
e
f
u
n
ctio
n
s
ar
e
h
er
e
r
e
f
er
r
ed
to
as
G
DM
_
MM
D,
GDM
_
MK
W
,
GDM
_
L
C
H,
G
DM
_
C
C
Y
an
d
GD
M_
NL
G
r
esp
ec
tiv
el
y
.
Fo
r
ec
asti
n
g
e
f
f
icie
n
c
y
is
j
u
d
g
ed
h
er
e
b
y
e
x
a
m
in
in
g
v
ar
io
u
s
e
f
f
icac
y
p
ar
am
eter
s
d
escr
ib
ed
b
r
ief
l
y
n
ex
t.
2
.
2
.
F
o
re
ca
s
t
ing
ef
f
ic
a
cy
pa
r
a
m
et
er
s
Ma
n
y
e
f
f
icac
y
p
ar
a
m
eter
s
ca
n
b
e
d
ef
i
n
ed
to
m
ea
s
u
r
e
d
e
g
r
ee
o
f
s
u
cc
e
s
s
i
n
f
o
r
ec
asti
n
g
.
L
et
y
d
d
en
o
te
th
e
ac
tu
al
s
to
c
k
p
r
ice
an
d
y
f
t
h
e
f
o
r
ec
asted
o
n
e.
T
h
e
er
r
o
r
in
f
o
r
ec
ast
is
th
e
n
g
i
v
e
n
b
y
e
=
(
y
d
–
y
f
)
.
L
e
t
‘
n
’
d
en
o
te
th
e
to
tal
n
u
m
b
er
o
f
in
p
u
t
-
o
u
tp
u
t
s
ets,
co
n
s
tr
u
cted
f
r
o
m
t
h
e
ti
m
e
s
er
ies
o
f
s
to
ck
p
r
ic
es.
L
et
t
h
e
m
ea
n
o
f
all
th
e
ac
t
u
al
s
to
ck
p
r
ices
b
ein
g
f
o
r
ec
asted
(
th
e
d
e
s
ir
ed
o
u
tp
u
t
s
)
b
e
d
en
o
ted
b
y
y
m
e
an
.
T
h
e
s
et
o
f
ef
f
icac
y
p
ar
am
eter
s
o
f
f
o
r
ec
ast
in
g
co
n
s
id
er
ed
h
er
e
to
in
v
esti
g
ate
e
f
f
ic
ien
c
y
o
f
A
I
m
et
h
o
d
s
ar
e
d
is
cu
s
s
ed
[
3
2
]
.
1.
Me
an
E
r
r
o
r
(
ME
)
ME=
1
n
∑
e
t
n
t=1
(
7
)
Me
an
er
r
o
r
(
ME
)
is
a
m
ea
s
u
r
e
o
f
t
h
e
a
v
er
ag
e
d
if
f
er
en
c
e
b
et
w
ee
n
th
e
ac
t
u
al
(
d
esire
d
)
p
r
ices
an
d
t
h
e
f
o
r
ec
asted
o
n
es
an
d
i
s
g
iv
e
n
i
n
(
7
)
.
As it
s
h
o
w
s
t
h
e
d
ir
ec
tio
n
o
f
er
r
o
r
it
m
a
y
also
b
e
ca
lled
f
o
r
ec
ast b
ias.
‘
ME
’
m
a
y
t
u
r
n
o
u
t to
b
e
d
ec
ep
tiv
el
y
s
m
all
a
s
p
o
s
itiv
e
a
n
d
n
e
g
ati
v
e
v
alu
e
s
o
f
i
n
d
iv
id
u
al
e
t
m
a
y
ca
n
ce
l e
ac
h
o
th
er
.
2.
Mean
A
b
s
o
lu
te
Dev
iat
io
n
(
M
A
D)
MA
D
=
1
n
∑
|
e
t
|
n
t=1
(
8
)
T
h
is
p
ar
a
m
eter
is
s
u
m
o
f
ab
s
o
lu
te
v
alu
e
s
o
f
er
r
o
r
s
an
d
is
g
iv
en
i
n
(
8
)
.
P
o
s
itiv
e
an
d
n
e
g
a
tiv
e
er
r
o
r
s
n
o
m
o
r
e
ca
n
ce
l
ea
ch
o
th
er
.
I
t
d
o
es
n
o
t
h
o
w
ev
er
in
d
icate
t
h
e
d
ir
ec
tio
n
o
f
er
r
o
r
s
.
Fo
r
a
g
o
o
d
f
o
r
ec
ast
‘
M
A
D
’
s
h
o
u
ld
b
e
m
ad
e
as s
m
all
as p
o
s
s
ib
le.
3.
Me
an
Sq
u
ar
e
E
r
r
o
r
(
MSE
)
MSE
=
1
n
∑
(
e
t
)
2
n
t=1
(
9
)
I
t
is
clea
r
f
r
o
m
t
h
e
ab
o
v
e
ex
p
r
ess
io
n
t
h
at
‘
M
SE’
i
s
th
e
av
er
ag
e
o
f
s
q
u
ar
es
o
f
f
o
r
ec
ast
er
r
o
r
s
an
d
is
g
iv
e
n
i
n
(
9
)
L
ar
g
e
i
n
d
iv
id
u
al
er
r
o
r
s
a
f
f
ec
t it
s
ig
n
i
f
ica
n
tl
y
.
T
h
is
p
ar
a
m
eter
d
o
es n
o
t
g
iv
e
an
y
id
ea
o
f
th
e
d
ir
ec
tio
n
o
f
t
h
e
o
v
er
all
er
r
o
r
.
4.
R
o
o
t M
ea
n
Sq
u
ar
e
E
r
r
o
r
(
R
MSE
)
R
MSE
=
√
MSE
(
1
0
)
R
MSE
co
n
tain
s
all
th
e
p
r
o
p
er
ties
o
f
M
SE
a
n
d
is
g
i
v
en
in
(
1
0
)
.
I
t
is
w
id
el
y
co
m
p
u
t
ed
an
d
r
ep
o
r
ted
in
liter
atu
r
e.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
I
n
t J
A
r
ti
f
I
n
tell
,
Vo
l.
9
,
No
.
1
,
Ma
r
ch
20
20
:
46
–
57
50
5.
Me
an
P
er
ce
n
t Fo
r
ec
ast E
r
r
o
r
(
MP
E
)
MP
E
=
1
n
∑
(
e
t
y
d
t
)
*
1
0
0
n
t=1
(
1
1
)
MP
E
is
in
d
ep
en
d
en
t
o
f
th
e
m
a
g
n
i
tu
d
e
o
f
th
e
p
r
ices
a
s
it
is
th
e
av
er
ag
e
o
f
p
er
ce
n
tag
e
o
f
f
o
r
ec
asti
n
g
er
r
o
r
s
an
d
is
d
ef
i
n
ed
in
(
1
1
)
.
I
t
in
d
icate
s
th
e
d
ir
ec
tio
n
o
f
er
r
o
r
.
I
n
d
iv
id
u
al
er
r
o
r
s
o
f
o
p
p
o
s
ite
s
ig
n
s
n
u
lli
f
y
ea
c
h
o
t
h
er
m
ak
in
g
it d
ec
ep
tiv
el
y
s
m
all.
L
ik
e
‘
ME
’
it
s
v
al
u
e
s
h
o
u
ld
al
s
o
b
e
k
ep
t a
s
s
m
al
l a
s
p
o
s
s
ib
le
f
o
r
a
g
o
o
d
f
o
r
ec
ast.
6.
Me
an
A
b
s
o
lu
te
P
er
ce
n
t Fo
r
ec
ast E
r
r
o
r
(
MA
P
E
)
MA
P
E
=
1
n
∑
|
(
e
t
y
d
t
)
*
1
0
0
|
n
t=1
(
12)
MA
P
E
g
i
v
es
th
e
a
v
er
ag
e
o
f
p
er
ce
n
tag
e
o
f
ab
s
o
lu
te
v
alu
e
s
o
f
in
d
i
v
id
u
al
er
r
o
r
s
in
f
o
r
ec
ast
an
d
is
g
iv
e
n
in
(
1
2
)
.
I
t
is
i
n
d
ep
en
d
en
t
o
f
th
e
s
ca
l
e
o
f
t
h
e
d
ata.
I
n
d
iv
id
u
al
er
r
o
r
s
o
f
o
p
p
o
s
ite
s
i
g
n
s
d
o
n
o
t
ca
n
ce
l
ea
c
h
o
t
h
er
.
Su
f
f
icien
tl
y
s
m
all
v
a
lu
e
o
f
‘
M
A
P
E
’
m
a
y
e
n
s
u
r
e
a
g
o
o
d
f
o
r
ec
ast.
7.
Me
an
P
er
ce
n
t
A
cc
u
r
ac
y
(
MP
A
)
MP
A
=
1
0
0
–
MA
P
E
(
1
3
)
‘
MP
A’
d
ep
en
d
s
o
n
‘
M
A
P
E
’
d
ir
ec
tl
y
.
I
t
is
d
e
f
i
n
ed
in
(
1
3
)
.
As
it
g
i
v
es
m
ea
n
p
er
ce
n
t
ac
cu
r
ac
y
a
n
d
n
o
t
th
e
er
r
o
r
,
it m
a
y
s
o
u
n
d
m
o
r
e
p
leas
in
g
to
s
o
m
e
u
s
er
s
.
8.
C
o
ef
f
icie
n
t
o
f
Dete
r
m
i
n
atio
n
(
R
2
)
R
2
= 1
-
∑
(
y
d
t
-
y
f
t
)
2
n
t
=
1
∑
(
y
d
t
-
y
m
e
a
n
)
2
n
t
=
1
(
1
4
)
R
2
is
a
m
ea
s
u
r
e
t
h
at
r
ep
r
esen
t
s
th
e
g
o
o
d
n
es
s
o
f
f
it
o
f
a
m
o
d
el
an
d
is
g
iv
e
n
i
n
(
1
4
)
.
L
ar
g
e
v
al
u
es
o
f
R
2
m
a
y
s
u
g
g
e
s
t a
g
o
o
d
f
it to
h
is
to
r
ical
d
ata.
I
t m
a
y
h
o
w
e
v
er
n
o
t b
e
s
o
w
h
ile
f
o
r
ec
asti
n
g
o
u
t o
f
s
a
m
p
le
d
ata
[
3
2
]
.
2
.
3
.
Da
t
a
c
o
llect
io
n a
nd
prepro
ce
s
s
ing
W
ee
k
l
y
ti
m
e
h
o
r
izo
n
h
a
s
b
ee
n
co
n
s
id
er
ed
in
th
e
p
r
esen
t
w
o
r
k
.
T
h
e
g
o
ld
p
r
ice
d
ata
is
d
o
w
n
lo
ad
ed
f
r
o
m
a
r
eliab
le
s
ite
o
n
i
n
v
esti
n
g
[
3
3
]
.
A
d
ata
w
i
n
d
o
w
o
f
4
y
ea
r
s
o
f
g
o
ld
p
r
ices,
f
r
o
m
J
an
2
0
1
5
to
Dec
2
0
1
8
,
h
as
b
ee
n
co
n
s
id
er
ed
h
er
e.
T
h
e
d
ata
co
n
s
is
t
s
o
f
t
h
e
p
r
ices
o
f
g
o
ld
f
o
r
th
e
f
ir
s
t
tr
ad
i
n
g
d
a
y
o
f
ev
er
y
w
ee
k
in
th
e
en
tire
ti
m
e
p
er
io
d
.
Pric
es
ar
e
n
o
r
m
ali
s
ed
b
et
w
ee
n
0
.
1
an
d
0
.
9
.
T
im
e
s
er
ies
f
o
r
m
atio
n
is
d
o
n
e
b
y
m
ak
i
n
g
s
ets
o
f
w
ee
k
l
y
p
r
ices
o
f
5
w
ee
k
s
as
in
p
u
t
an
d
th
e
p
r
ice
o
f
th
e
6
th
w
ee
k
as
th
e
co
r
r
esp
o
n
d
in
g
o
u
t
p
u
t.
T
im
e
s
er
ies
s
o
f
o
r
m
ed
ar
e
d
iv
id
ed
in
th
r
ee
c
ateg
o
r
ies:
tr
ain
i
n
g
,
test
i
n
g
an
d
v
alid
atio
n
.
T
r
ain
i
n
g
an
d
test
i
n
g
s
er
ie
s
co
n
s
tit
u
t
e
ab
o
u
t
in
itial
8
0
%
o
f
t
h
e
to
tal.
A
b
o
u
t
7
0
%
o
f
t
h
ese
s
er
ies
ar
e
r
an
d
o
m
l
y
s
elec
ted
f
o
r
tr
ain
i
n
g
t
h
e
n
et
w
o
r
k
a
n
d
th
e
r
e
m
ain
in
g
3
0
%
ar
e
u
s
ed
f
o
r
test
in
g
.
Valid
atio
n
s
er
ie
s
c
o
r
r
esp
o
n
d
to
ch
r
o
n
o
lo
g
icall
y
th
e
late
s
t
d
ata
a
n
d
co
n
s
ti
t
u
te
ab
o
u
t
2
0
%
o
f
th
e
to
tal.
T
h
e
v
alid
atio
n
d
ata
is
th
u
s
n
o
t
co
n
tain
ed
in
t
h
e
tr
ain
i
n
g
a
n
d
test
in
g
d
ata
an
d
is
r
ef
er
r
ed
to
,
h
er
e,
as
o
u
t
o
f
s
a
m
p
le
d
ata.
Fo
r
ec
asti
n
g
ac
cu
r
ac
y
w
ill
b
e
e
x
a
m
i
n
ed
f
o
r
v
ar
y
i
n
g
v
alid
atio
n
p
er
io
d
s
.
3.
RE
SU
L
T
S
AND
D
I
SCU
SS
I
O
N
I
n
th
e
p
r
ese
n
t
s
tu
d
y
th
e
o
n
e
w
ee
k
a
h
ea
d
p
r
ice
o
f
g
o
ld
is
fo
r
ec
a
st
ed
f
r
o
m
t
h
e
p
r
ev
io
u
s
5
w
ee
k
s
’
p
r
ices
u
s
in
g
th
e
clas
s
ical
AN
N
m
e
th
o
d
s
a
n
d
t
h
e
m
o
d
if
ied
GDM
m
et
h
o
d
s
f
o
r
v
ar
io
u
s
ANN
ar
ch
itec
tu
r
es.
T
h
e
w
o
r
k
d
o
n
e
i
s
ca
teg
o
r
ized
as b
elo
w
an
d
d
is
c
u
s
s
ed
in
d
etail
i
n
s
ec
tio
n
s
3
.
1
to
3
.
3
.
1.
Fo
r
ec
ast
o
f
w
ee
k
l
y
p
r
ices
o
f
g
o
ld
u
s
in
g
cla
s
s
ical
ANN
al
g
o
r
ith
m
s
n
a
m
el
y
G
DM
,
R
P
,
S
C
G,
L
M,
B
R
,
B
FGS,
an
d
OSS.
2.
I
m
p
le
m
e
n
tatio
n
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
if
ied
GDM
m
e
th
o
d
s
t
o
in
cr
ea
s
e
f
o
r
ec
asti
n
g
e
f
f
icie
n
c
y
an
d
i
n
ter
-
co
m
p
ar
is
o
n
o
f
t
h
e
r
esu
lts
o
b
tain
ed
w
ith
t
h
o
s
e
o
b
tain
ed
b
y
cl
ass
ical
GDM
.
3.
C
o
m
p
ar
is
o
n
w
it
h
t
h
e
w
o
r
k
d
o
n
e
b
y
o
th
er
r
esear
c
h
er
s
f
o
r
g
o
ld
f
o
r
ec
asti
n
g
u
s
in
g
tr
a
d
itio
n
al
A
NN
m
et
h
o
d
s
.
3
.
1
.
F
o
re
ca
s
t
ing
us
ing
cla
s
s
i
ca
l A
NN
a
lg
o
rit
h
m
s
Fo
r
ec
asti
n
g
o
f
w
ee
k
l
y
g
o
ld
p
r
ices
h
as
b
ee
n
d
o
n
e
u
s
i
n
g
th
e
c
lass
ical
A
NN
alg
o
r
it
h
m
s
n
a
m
el
y
G
DM
,
R
P
,
SC
G,
L
M,
B
R
,
B
FG
S,
O
SS
w
it
h
t
h
e
ar
c
h
itect
u
r
e
05
-
03
-
0
1
.
E
f
f
icac
y
p
ar
a
m
eter
s
o
f
f
o
r
ec
asti
n
g
o
b
tain
ed
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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51
f
o
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test
i
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g
a
n
d
v
alid
atio
n
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h
a
s
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ar
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ar
ized
in
T
ab
les
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u
r
e
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o
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tain
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i
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ase
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le
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u
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g
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e
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m
u
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in
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b
y
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y
i
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ith
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a
n
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8
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0
3
)
an
d
t
h
e
m
ax
i
m
u
m
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ar
e
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y
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ith
m
.
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ab
le
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f
f
icac
y
p
ar
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m
eter
s
o
f
f
o
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asti
n
g
o
f
g
o
ld
p
r
ices u
s
in
g
A
NN
(
0
5
-
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0
1
)
in
test
in
g
p
h
ase
A
N
N
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e
t
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d
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M
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M
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M
0
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1
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6
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G
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Fig
u
r
e
1
.
C
o
m
p
ar
is
o
n
o
f
MP
A,
MSE
an
d
R
2
in
t
h
e
test
i
n
g
p
h
ase
o
f
g
o
ld
p
r
ice
f
o
r
ec
ast f
o
r
class
ical
m
et
h
o
d
s
Fu
r
t
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er
,
th
e
r
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lt
s
w
er
e
v
a
lid
ated
o
n
an
o
u
t
o
f
s
a
m
p
l
e
d
ata
(
v
alid
atio
n
p
h
ase)
also
f
o
r
th
e
ch
r
o
n
o
lo
g
icall
y
la
test
4
6
w
ee
k
s
.
A
l
l
t
h
e
e
f
f
icac
y
p
ar
a
m
ete
r
s
ex
ce
p
t
R
2
ar
e
s
h
o
w
n
in
T
ab
le
2
.
R
2
is
n
o
t
a
r
eliab
le
p
er
f
o
r
m
a
n
ce
in
d
i
ca
to
r
f
o
r
th
e
o
u
t o
f
s
a
m
p
le
d
ata.
T
ab
le
2
.
E
f
f
icac
y
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ar
a
m
eter
s
o
f
f
o
r
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asti
n
g
o
f
g
o
ld
p
r
ices u
s
in
g
A
NN
0
5
-
03
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0
1
in
v
alid
ati
o
n
p
h
ase
A
N
N
M
e
t
h
o
d
ME
M
A
D
M
S
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R
M
S
E
M
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M
A
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E%
M
P
A
%
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D
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0
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0
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7
6
0
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5
0
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0
5
6
6
4
.
6
1
5
.
7
2
9
4
.
2
8
RP
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0
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5
6
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2
0
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2
3
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3
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.
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2
4
.
8
6
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.
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C
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0
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0
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5
0
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3
1
.
9
6
6
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9
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3
.
7
1
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0
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.
7
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0
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u
r
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MP
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a
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d
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o
b
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ed
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n
t
h
e
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n
p
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ase
f
o
r
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h
e
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g
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r
ith
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t
c
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e
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ee
n
f
r
o
m
T
ab
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o
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e
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d
Fig
u
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e
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at
in
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e
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th
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d
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%
in
T
e
s
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Phas
e
0
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0
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5
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Me
th
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d
R
2
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n
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ti
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Phas
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
5
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8938
I
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r
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20
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:
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–
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52
Fig
u
r
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2
.
P
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f
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o
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et
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As
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t
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r
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l
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ap
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el
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o
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ata
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ap
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g
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r
e
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er
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s
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r
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asted
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o
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m
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lized
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r
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o
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h
a
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a
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ase
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o
r
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R
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g
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m
w
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h
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h
e
A
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n
f
i
g
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r
atio
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u
r
e
3
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Desire
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v
/s
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t f
o
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ata
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-
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01
3
.
2
.
F
o
re
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t
ing
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ing
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he
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ed
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lg
o
rit
h
m
s
a
n
d inte
r
-
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m
pa
riso
n w
it
h c
la
s
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ica
l G
DM
Fo
r
ec
asti
n
g
h
a
s
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ee
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e
u
s
i
n
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th
e
5
n
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v
e
l
m
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d
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ied
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al
g
o
r
ith
m
s
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GD
M_
MM
D,
GDM
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MK
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L
C
H,
G
DM
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C
C
Y
a
n
d
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_
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d
is
cu
s
s
ed
in
s
ec
tio
n
2
.
1
w
it
h
v
a
r
io
u
s
ar
ch
itect
u
r
es.
T
h
ese
r
esu
lt
s
ar
e
co
m
p
ar
ed
w
i
th
t
h
o
s
e
o
f
t
h
e
cla
s
s
ical
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r
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lt
s
g
i
v
e
n
i
n
Sectio
n
3
.
1
.
E
f
f
icac
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ar
a
m
eter
s
o
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g
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n
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tio
n
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ase
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ized
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a
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les 3
an
d
4
.
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ab
le
3
.
Fo
r
ec
asti
n
g
p
er
f
o
r
m
a
n
ce
d
u
r
in
g
tes
tin
g
p
h
a
s
e
o
f
cla
s
s
ical
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a
n
d
m
o
d
i
f
ied
m
et
h
o
d
s
o
f
GDM
w
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h
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ar
io
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n
f
i
g
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r
atio
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o
f
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NN
f
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r
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A
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e
t
h
o
d
A
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r
c
h
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t
e
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t
u
r
e
M
S
E
(
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e
st
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h
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se
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P
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%
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g
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h
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se
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2
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T
e
st
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h
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se
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l
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l
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93
93
94
94
95
95
96
96
GDM
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B
F
G
S
BR
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S
S
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%
A
N
N
Me
th
o
d
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%
in
V
ali
d
ati
o
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h
as
e
0
,
0
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0
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3
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4
GDM
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A
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N
Me
th
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d
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ali
d
ati
o
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h
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e
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1
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,
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4
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6
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7
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1
6
11
16
21
26
31
36
41
46
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u
tp
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n
t N
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Phas
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J
A
r
ti
f
I
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tell
I
SS
N:
2252
-
8938
A
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b
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meth
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... (
S
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53
T
ab
le
3
.
Fo
r
ec
asti
n
g
p
er
f
o
r
m
a
n
ce
d
u
r
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tes
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g
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h
a
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ical
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a
n
d
m
o
d
i
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ied
m
et
h
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d
s
o
f
GDM
w
ith
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ar
io
u
s
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n
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ig
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r
ati
o
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s
o
f
A
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f
o
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ld
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e
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se
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se
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3
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at
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p
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ase
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m
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m
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th
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f
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e
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A
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r
e
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ith
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is
s
h
o
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n
g
r
ap
h
icall
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in
Fi
g
u
r
e
4.
Fig
u
r
e
4
.
C
o
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p
ar
is
o
n
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f
MP
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MSE
an
d
R
2
in
t
h
e
tes
tin
g
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h
ase
o
f
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o
ld
p
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ast f
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r
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d
m
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ied
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eth
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t
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n
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e
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g
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4
,
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e,
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e
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s
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MP
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y
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e
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C
H
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e
th
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d
w
ith
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e
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1
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e
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als
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ai
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e
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asts
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t
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I
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tell
,
Vo
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9
,
No
.
1
,
Ma
r
ch
20
20
:
46
–
57
54
T
ab
le
4
.
Fo
r
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asti
n
g
P
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f
o
r
m
a
n
ce
d
u
r
in
g
Valid
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P
h
ase
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f
clas
s
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a
n
d
m
o
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if
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m
eth
o
d
s
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d
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a
n
th
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et
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s
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a
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s
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r
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d
4
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s
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p
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s
also
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m
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if
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et
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d
s
g
i
v
e,
in
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e
n
er
al,
b
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M
P
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th
a
n
th
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.
GD
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C
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o
r
ith
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ter
m
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t
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9
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ar
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ith
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h
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Fi
g
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r
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5.
Fig
u
r
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.
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f
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d
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ase
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d
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_
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ith
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w
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itect
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ith
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ase
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ase
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ith
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ab
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s
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Evaluation Warning : The document was created with Spire.PDF for Python.