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t'
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n
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ial
c
a
p
a
c
it
y
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irst
ly
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th
e
p
rice
f
o
re
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a
stin
g
p
ro
c
e
d
u
re
s
f
o
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t
h
e
e
x
trem
e
g
ra
d
ien
t
b
o
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sti
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g
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Bo
o
st),
g
a
ted
re
c
u
rre
n
t
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it
(G
RU),
a
n
d
h
y
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ri
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EM
m
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ls
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l
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ra
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th
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l
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ted
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g
g
le
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d
e
_
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P
rice
a
n
d
KL_
a
p
a
rtme
n
t).
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h
is
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y
th
e
n
p
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m
b
i
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th
e
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rice
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fo
rm
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term
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se
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a
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ly
sis.
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p
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tal
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th
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ted
m
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e
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n
p
rice
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c
a
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g
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c
c
u
ra
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y
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K
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w
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r
d
s
:
AR
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MA
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x
tr
em
e
g
r
a
d
ien
t b
o
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s
tin
g
Gate
d
r
ec
u
r
r
e
n
t u
n
it
Pre
d
ictio
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Pric
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f
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ec
asti
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g
T
h
is i
s
a
n
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p
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n
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c
c
e
ss
a
rticle
u
n
d
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r th
e
CC B
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SA
li
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e
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se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
Kh
air
u
l A
zh
ar
Kasm
ir
an
Fac
u
lty
o
f
C
o
m
p
u
ter
Scien
ce
an
d
I
n
f
o
r
m
atio
n
T
ec
h
n
o
lo
g
y
,
Un
iv
er
s
iti Pu
tr
a
Ma
lay
s
ia
Selan
g
o
r
,
Ma
lay
s
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E
m
ail:
k
_
az
h
ar
@
u
p
m
.
ed
u
.
m
y
1.
I
NT
RO
D
UCT
I
O
N
Pric
e
f
o
r
ec
asti
n
g
is
ess
en
tial
an
d
cr
itical.
H
o
wev
er
,
th
e
k
e
y
q
u
esti
o
n
is
wh
at
t
h
e
b
est
p
r
ed
ictio
n
m
eth
o
d
is
an
d
wh
eth
er
it
ca
n
b
e
o
p
tim
ized
f
o
r
g
r
ea
ter
ac
c
u
r
ac
y
.
Ad
d
itio
n
ally
,
wh
ic
h
f
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cto
r
s
o
r
in
d
icato
r
s
in
f
lu
en
ce
p
r
ice
th
e
m
o
s
t
an
d
s
h
o
u
ld
b
e
p
r
io
r
itized
in
th
e
ca
lcu
latio
n
s
tep
s
,
g
iv
en
th
e
wid
e
r
an
g
e
o
f
c
o
m
p
lex
an
d
d
y
n
a
m
ic
f
ac
to
r
s
.
B
y
lev
er
ag
in
g
ar
tific
ial
in
tellig
en
ce
(
AI
)
alg
o
r
ith
m
s
,
b
u
s
in
ess
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ca
n
en
h
an
ce
p
r
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f
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ac
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m
itig
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n
d
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atin
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ca
s
h
in
f
lo
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d
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an
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m
ak
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b
etter
d
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d
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f
in
an
ci
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g
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a
n
d
o
th
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f
in
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cial
s
tr
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Fu
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th
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m
o
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e,
it
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ch
allen
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in
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to
estab
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h
a
s
u
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elatio
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s
h
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b
etwe
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in
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ex
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f
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an
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p
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ev
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o
f
th
e
m
en
tio
n
e
d
f
ac
to
r
s
o
n
p
r
ices
[
1
]
–
[
3
]
,
b
u
t
AI
ca
n
h
elp
.
A
r
em
ar
k
ab
le
m
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el,
ex
tr
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m
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r
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h
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m
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m
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with
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v
an
tag
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b
ec
au
s
e
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f
its
m
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h
an
is
m
[
4
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.
Firstl
y
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b
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s
e
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f
its
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s
em
b
le
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s
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m
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g
co
n
v
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tio
n
al
m
ac
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e
lear
n
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g
(
ML
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alg
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r
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m
s
.
Seco
n
d
,
it
in
te
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r
ates
r
eg
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lar
iz
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s
tr
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,
in
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in
g
L
1
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d
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r
e
g
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lar
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d
im
p
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tio
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ally
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t
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f
f
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m
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d
f
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m
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in
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ce
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r
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tio
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m
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el
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ter
p
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I
t
also
d
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m
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d
f
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r
im
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o
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p
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c
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in
g
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T
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last
f
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tu
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XG
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s
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p
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
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I
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tif
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n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
1
3
1
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3
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3
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XG
B
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s
t
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a
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m
m
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d
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p
tio
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f
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p
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ed
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wo
r
k
lo
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s
b
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a
u
s
e
o
f
its
s
tab
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y
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ter
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d
s
ca
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l
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[
5
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p
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ed
a
n
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m
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th
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d
th
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s
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X
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ML
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to
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m
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d
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p
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r
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(
B
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h
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f
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d
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ca
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t
h
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J
in
et
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.
[
6
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aim
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to
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p
a
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em
ic
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s
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ev
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th
r
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m
b
in
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f
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r
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m
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co
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tio
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C
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ter
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with
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t
h
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eliab
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a
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s
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m
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d
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in
f
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ec
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p
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tr
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s
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wad
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s
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r
esear
ch
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ac
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r
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f
f
o
r
ec
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[
7
]
–
[
9
]
.
I
n
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two
ty
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[
1
0
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,
[
1
1
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.
I
n
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tific
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Yaq
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[
1
2
]
d
is
cu
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m
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ar
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p
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ac
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[
1
3
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T
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1
4
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k
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ch
allen
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p
r
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r
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ased
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2.
M
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=
A
VG
(
AF
+
ф
+
Ơ
i
)
×
W
i
(
1
)
W
h
er
e
AVG
i
s
av
er
ag
e
f
u
n
ctio
n
;
AF
is
AR
I
MA
f
o
r
ec
asti
n
g
o
f
th
e
f
o
r
ec
asted
p
er
io
d
;
Ф
is
th
e
v
alu
e
o
f
th
e
s
am
e
p
er
io
d
;
Ơ
is
th
e
v
alu
e
o
f
th
e
n
ex
t p
e
r
io
d
;
an
d
W
is
weig
h
t r
atio
.
T
h
e
weig
h
t w
ill b
e
co
m
p
u
ted
t
h
r
o
u
g
h
(
2
).
α
=
A
VG
(
TS
)
(
2
)
W
h
er
e
T
S
is
tim
e
s
er
ies
:
th
e
wh
o
le
p
er
io
d
o
f
th
e
s
elec
ted
t
im
e
s
er
ies.
T
h
en
,
g
et
th
e
s
ig
m
o
id
o
f
α
as
d
ef
in
e
d
in
(
3
).
W
=
1
+
1
1
e
−
α
(
3
)
T
h
e
f
o
r
ec
asti
n
g
m
et
h
o
d
o
lo
g
y
lev
er
ag
in
g
th
e
p
r
o
p
o
s
ed
h
y
b
r
i
d
-
AR
I
MA
-
E
M
m
o
d
el
ca
n
b
e
co
n
cisely
s
u
m
m
ar
ized
as:
i)
Pre
p
ar
e
th
e
d
ataset
:
t
h
e
r
elev
an
t
d
ata
is
ex
tr
ac
ted
:
two
v
ar
iab
les
s
tar
t_
y
ea
r
an
d
en
d
_
y
e
ar
d
ef
in
e
th
e
r
an
g
e
o
f
y
ea
r
s
to
ex
tr
ac
t
f
r
o
m
th
e
d
ataset.
R
o
ws
will
b
e
s
elec
ted
f
r
o
m
th
e
d
ataset
wh
er
e
th
e
'
Yea
r
'
co
lu
m
n
is
g
r
ea
ter
th
an
o
r
eq
u
a
l to
s
tar
t_
y
ea
r
an
d
less
th
an
o
r
eq
u
al
to
en
d
_
y
ea
r
.
ii)
C
alcu
latin
g
th
e
av
e
r
ag
e
tim
e
s
er
ies
len
g
th
:
t
h
e
n
u
m
b
er
o
f
r
o
ws
in
th
e
d
ataset
is
d
eter
m
in
e
d
an
d
u
s
ed
to
ca
lcu
late
th
e
v
ar
iab
le
AVG(
T
S).
iii)
Per
f
o
r
m
AR
I
MA
f
o
r
ec
asti
n
g
:
a
n
ar
r
ay
AR
I
MA
f
o
r
ec
asti
n
g
is
cr
ea
ted
an
d
in
itialized
with
a
s
er
ies
o
f
n
u
m
er
ical
v
alu
es r
e
p
r
esen
tin
g
th
e
AR
I
MA
f
o
r
ec
asti
n
g
d
ata.
iv
)
Dete
r
m
in
e
alp
h
a
or
:
t
h
e
v
ar
i
ab
le
alp
h
a
is
ass
ig
n
ed
th
e
v
alu
e
o
f
AVG(
T
S),
r
ep
r
esen
tin
g
th
e
av
er
ag
e
tim
e
s
er
ies len
g
th
ca
lcu
lated
e
ar
lier
.
v)
C
alcu
late
weig
h
t
:
a
p
p
ly
in
g
s
ig
m
o
id
ex
p
o
n
e
n
tial
f
u
n
ctio
n
will
m
ak
e
th
e
d
ata
r
an
g
e
f
all
b
etwe
en
0
to
1
wh
ich
is
ea
s
y
to
illu
s
tr
ate
in
th
e
g
r
ap
h
an
d
f
ac
ilit
ates c
alcu
latio
n
s
.
v
i)
C
alcu
late
f
o
r
ec
asted
v
alu
es
:
t
h
e
'
C
r
u
d
e
Oil
Pric
e
'
co
lu
m
n
v
alu
es
ar
e
ex
tr
ac
ted
f
r
o
m
th
e
d
ataset
an
d
ass
ig
n
ed
to
th
e
v
ar
ia
b
le
Ф
.
v
ii)
T
h
e
p
r
o
ce
s
s
s
h
if
t
(
-
1
)
s
tep
:
wh
er
e
s
elec
tin
g
th
e
y
ea
r
to
s
h
if
t
t
h
e
'
C
r
u
d
e
Oil
Pric
e'
co
lu
m
n
v
alu
es
o
n
e
s
tep
f
o
r
war
d
,
an
d
ass
ig
n
s
th
em
to
th
e
v
ar
iab
le
Ơ.
v
iii)
T
h
e
f
o
r
ec
asted
v
alu
es
ar
e
c
alcu
lated
b
y
ap
p
ly
i
n
g
th
e
s
u
g
g
ested
eq
u
atio
n
t
o
th
e
ar
r
ay
s
AR
I
MA
f
o
r
ec
asti
n
g
,
Ф
,
an
d
Ơ
alo
n
g
with
t
h
e
weig
h
t a
r
r
a
y
W
.
T
o
s
u
m
u
p
th
e
wh
o
le
p
r
o
g
r
ess
in
s
h
o
r
t p
o
in
ts
:
i)
T
h
e
h
y
b
r
i
d
-
AR
I
MA
-
E
M
eq
u
atio
n
co
m
b
i
n
es
th
e
AR
I
MA
f
o
r
ec
asti
n
g
with
a
d
d
itio
n
al
co
m
p
o
n
en
ts
(
ф
an
d
Ơ
)
an
d
weig
h
ts
(
W
i)
to
g
e
n
er
ate
f
o
r
ec
asts
.
ii)
T
h
e
weig
h
ts
a
r
e
d
eter
m
in
ed
b
y
av
e
r
ag
in
g
th
e
en
tire
tim
e
s
e
r
ies
an
d
ap
p
ly
i
n
g
a
s
ig
m
o
i
d
tr
an
s
f
o
r
m
atio
n
to
th
e
av
er
a
g
e.
iii)
T
h
is
ap
p
r
o
ac
h
aim
s
to
in
co
r
p
o
r
ate
b
o
th
h
is
to
r
ical
d
ata
(
AR
I
MA
f
o
r
ec
asti
n
g
)
an
d
ad
d
itio
n
al
f
ac
to
r
s
(
ф
an
d
Ơ
)
in
to
th
e
f
o
r
ec
asti
n
g
p
r
o
ce
s
s
,
with
weig
h
ts
ad
ju
s
ted
b
ased
o
n
th
e
a
v
er
ag
e
b
eh
a
v
io
r
o
f
tim
e
s
er
ies.
2.
2
.
1
.
P
re
dict
io
n r
esu
lt
s
co
m
pa
riso
n a
nd
ev
a
lua
t
io
n
W
h
en
ev
alu
atin
g
th
e
ef
f
ec
tiv
en
ess
o
f
d
if
f
er
en
t
f
o
r
ec
asti
n
g
m
o
d
els,
it
is
ess
en
tia
l
to
q
u
an
tify
th
eir
ac
cu
r
ac
y
.
T
h
is
is
ty
p
ically
ac
h
iev
ed
b
y
co
m
p
a
r
in
g
th
eir
f
o
r
ec
asts
ag
ain
s
t
th
e
ac
tu
al
o
b
s
er
v
ed
v
alu
es
u
s
in
g
s
tatis
t
ical
m
etr
ics.
T
wo
co
m
m
o
n
m
etr
ics
u
s
ed
f
o
r
th
is
p
u
r
p
o
s
e
ar
e
r
o
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
an
d
m
ea
n
ab
s
o
lu
te
p
er
ce
n
ta
g
e
e
r
r
o
r
(
M
APE)
,
as sh
o
wn
in
(
4
)
an
d
(
5
).
R
M
SE
=
√
∑
(
x
i
N
i
=
1
−
Ý
i
)
2
N
(
4
)
W
h
er
e
v
ar
iab
le
v
alu
es
;
is
th
e
n
u
m
b
er
o
f
n
o
n
-
m
is
s
in
g
d
ata
p
o
in
ts
;
is
an
ac
tu
al
o
b
s
er
v
ati
o
n
tim
e
s
er
ies
;
an
d
Ý
is
an
esti
m
ated
tim
e
s
er
ies
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8
9
3
8
I
n
t J Ar
tif
I
n
tell
,
Vo
l.
15
,
No
.
4
,
Au
g
u
s
t 2
0
2
6
:
3
1
3
1
-
3
1
4
3
3134
M
A
PE
=
1
n
∑
|
A
t
−
F
t
A
t
|
n
i
=
1
(
5
)
W
h
er
e
A
t
is
ac
tu
al
v
alu
e
;
F
t
is
f
o
r
ec
ast v
alu
e
; a
n
d
n
is
n
u
m
b
er
o
f
tim
es th
e
s
u
m
m
atio
n
iter
atio
n
h
ap
p
en
s
.
R
MSE
m
ea
s
u
r
es
th
e
av
e
r
ag
e
m
ag
n
itu
d
e
o
f
th
e
er
r
o
r
s
b
etw
ee
n
p
r
ed
icted
an
d
o
b
s
er
v
ed
v
alu
es.
I
t
is
co
m
p
u
ted
b
y
tak
in
g
th
e
s
q
u
a
r
e
r
o
o
t
o
f
th
e
a
v
er
ag
e
o
f
th
e
s
q
u
ar
ed
d
if
f
er
e
n
ce
s
b
etwe
en
p
r
ed
icted
(
Ý
)
an
d
o
b
s
er
v
ed
(
)
v
alu
es,
d
iv
id
e
d
b
y
th
e
to
tal
n
u
m
b
er
o
f
o
b
s
e
r
v
atio
n
s
(
)
.
T
h
is
p
r
o
v
id
es
a
s
in
g
le
n
u
m
b
er
r
ep
r
esen
tin
g
th
e
ty
p
ical
m
a
g
n
itu
d
e
o
f
e
r
r
o
r
s
i
n
th
e
f
o
r
ec
a
s
t.
W
h
er
ea
s
MA
PE
m
ea
s
u
r
es
th
e
ac
c
u
r
ac
y
o
f
a
f
o
r
ec
asti
n
g
m
o
d
el
as
a
p
er
ce
n
tag
e
o
f
th
e
ab
s
o
lu
te
er
r
o
r
r
elat
iv
e
to
th
e
ac
tu
al
v
alu
es.
I
t
is
c
alcu
lated
b
y
tak
i
n
g
th
e
m
ea
n
o
f
th
e
ab
s
o
lu
te
p
er
c
en
tag
e
er
r
o
r
s
b
etwe
en
ac
tu
al
(
At)
an
d
f
o
r
ec
asted
(
Ft)
v
alu
es
,
av
er
ag
i
n
g
o
v
er
all
o
b
s
er
v
atio
n
s
(
n
)
.
Usi
n
g
th
e
h
y
b
r
i
d
-
AR
I
MA
-
E
M
p
r
ed
ictio
n
p
r
o
ce
s
s
,
Fig
u
r
es
1
a
n
d
2
illu
s
tr
ate
th
e
y
ea
r
ly
a
n
d
m
o
n
th
ly
f
o
r
ec
asti
n
g
o
u
tco
m
es
f
o
r
th
e
y
ea
r
s
2
0
1
5
-
2
0
2
2
ap
p
lied
to
th
e
s
elec
ted
d
ataset
(
C
r
u
d
e_
Oil_
Pric
e)
.
Fig
u
r
e
1
.
Fo
r
ec
asted
y
ea
r
s
(
2
0
1
5
-
2
0
2
2
)
b
y
u
s
in
g
th
e
h
y
b
r
i
d
-
AR
I
MA
-
E
M
m
o
d
el
Fig
u
r
e
2
.
Mo
n
th
ly
f
o
r
ec
asti
n
g
f
o
r
th
e
y
ea
r
s
2
0
1
5
-
2
0
2
2
f
o
r
th
e
C
r
u
d
e_
Oil_
Pric
e
d
ataset
b
y
u
s
in
g
h
ybr
id
-
AR
I
MA
-
E
M
m
o
d
el
2
.
3
.
E
x
t
re
m
e
g
r
a
dient
bo
o
s
t
ing
XGBo
o
s
t
is
a
p
o
wer
f
u
l
f
o
r
ec
asti
n
g
m
o
d
el
with
s
ev
er
al
im
p
r
ess
iv
e
ad
v
an
ta
g
es.
Firstl
y
,
i
t
d
eliv
er
s
s
u
p
er
io
r
p
er
f
o
r
m
a
n
ce
co
m
p
ar
ed
to
tr
ad
itio
n
al
ML
alg
o
r
it
h
m
s
d
u
e
to
its
en
s
em
b
le
n
at
u
r
e
an
d
o
p
tim
ize
d
im
p
lem
en
tatio
n
.
Seco
n
d
ly
,
it
u
s
es
r
eg
u
lar
izatio
n
m
eth
o
d
s
li
k
e
L
1
an
d
L
2
to
r
ed
u
ce
o
v
er
f
itti
n
g
an
d
en
h
an
ce
its
ab
ilit
y
to
g
en
e
r
alize
[
1
5
]
.
Ad
d
itio
n
ally
,
XGBo
o
s
t
in
clu
d
es
a
f
ea
tu
r
e
im
p
o
r
tan
ce
ass
ess
m
en
t
m
ec
h
an
is
m
,
wh
ich
aid
s
in
m
o
d
el
in
ter
p
r
etatio
n
an
d
f
ea
tu
r
e
s
elec
tio
n
.
I
t
also
h
an
d
les
m
is
s
in
g
v
alu
es
ef
f
ec
tiv
ely
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
t J Ar
tif
I
n
tell
I
SS
N:
2252
-
8
9
3
8
Hyb
r
id
iz
a
tio
n
o
f h
yb
r
id
-
A
R
I
MA
-
E
M a
n
d
X
GB
o
o
s
t fo
r
en
h
a
n
ce
d
p
r
ice
p
r
ed
ictive
…
(
I
s
a
m
A
h
med
M.
Ya
q
o
o
b
)
3135
elim
in
atin
g
th
e
n
ee
d
f
o
r
d
ata
i
m
p
u
tatio
n
o
r
p
r
ep
r
o
ce
s
s
in
g
[
1
6
]
.
L
astl
y
,
XGBo
o
s
t
s
u
p
p
o
r
ts
p
ar
allel
p
r
o
ce
s
s
in
g
,
allo
win
g
ef
f
icien
t
tr
ain
in
g
o
n
lar
g
e
d
atasets
an
d
s
ig
n
if
ic
an
tly
cu
ttin
g
d
o
wn
c
o
m
p
u
tatio
n
al
tim
e.
T
h
ese
ch
ar
ac
ter
is
tics
co
llectiv
ely
m
ak
e
XGBo
o
s
t
a
f
av
o
r
ed
ch
o
ice
f
o
r
f
o
r
ec
asti
n
g
task
s
,
o
f
f
er
in
g
s
ca
lab
ilit
y
,
r
o
b
u
s
tn
ess
,
an
d
in
te
r
p
r
etab
ilit
y
[
1
7
]
.
T
h
e
XGBo
o
s
t
f
o
r
ec
asti
n
g
m
o
d
el
h
as
s
ev
er
al
b
e
n
ef
its
,
b
u
t
it
also
h
as
ce
r
tain
lim
itatio
n
s
.
T
h
e
f
ir
s
t
is
th
at
it
is
co
m
p
licated
,
wh
ic
h
co
u
l
d
b
e
d
if
f
ic
u
lt
f
o
r
in
e
x
p
er
ien
ce
d
u
s
er
s
to
u
n
d
er
s
tan
d
an
d
a
d
ju
s
t
th
e
p
ar
am
eter
s
.
Seco
n
d
ly
,
th
er
e
is
th
e
co
m
p
u
tatio
n
ally
d
em
an
d
in
g
p
a
r
t
o
f
tr
ain
in
g
a
n
XGBo
o
s
t
m
o
d
el,
p
ar
ticu
lar
ly
wh
en
wo
r
k
in
g
w
ith
h
u
g
e
d
atasets
o
r
h
ig
h
-
d
i
m
en
s
io
n
al
f
ea
tu
r
e
s
p
ac
es,
wh
ich
co
u
ld
ca
ll
f
o
r
a
s
u
b
s
tan
tial a
m
o
u
n
t o
f
p
r
o
ce
s
s
in
g
p
o
we
r
[
1
8
]
.
2
.
3
.
1
.
XG
B
o
o
s
t
in t
im
e
s
er
ies predict
io
n
I
n
ter
m
s
o
f
ex
am
i
n
in
g
th
e
p
o
wer
o
f
th
e
XGBo
o
s
t
m
o
d
el
in
tim
e
s
er
ies
f
o
r
ec
asti
n
g
,
th
e
m
o
d
el
will
b
e
ap
p
lied
to
th
e
s
elec
ted
d
ataset,
wh
ich
is
th
e
C
r
u
d
e_
Oil_
Pric
e
d
ataset
f
o
r
th
e
y
ea
r
s
2
0
1
5
-
2
0
2
3
f
r
o
m
th
e
Kag
g
le
web
s
ite.
T
h
e
s
tep
s
o
f
th
e
p
r
o
ce
s
s
ar
e
as
f
o
llo
ws
th
at
p
er
f
o
r
m
s
a
tim
e
s
er
ies
f
o
r
ec
asti
n
g
task
f
o
r
th
e
s
elec
ted
d
ataset
b
y
u
s
in
g
th
e
XGBo
o
s
t a
lg
o
r
ith
m
to
f
o
r
ec
ast th
e
y
ea
r
s
2
0
1
5
-
2
0
2
2
,
as in
T
ab
le
1
an
d
Fig
u
r
e
3
.
i)
Data
lo
ad
in
g
an
d
p
r
ep
ar
atio
n
:
lo
ad
s
a
d
ataset
co
n
tain
in
g
h
is
to
r
ical
cr
u
d
e
o
il
p
r
ices
an
d
s
ets
th
e
r
elev
an
t
co
lu
m
n
(
y
ea
r
an
d
c
r
u
d
e
o
il
p
r
ice
)
as
a
p
r
im
e
co
lu
m
n
th
at
w
ill
b
e
u
s
ed
to
an
aly
ze
an
d
f
o
r
ec
ast
th
e
n
ew
v
alu
es f
o
r
th
e
d
eter
m
in
e
d
r
esu
lt.
ii)
T
r
ain
-
test
s
p
lit:
th
e
d
ataset
will
b
e
s
p
lit
i
n
to
tr
ai
n
in
g
an
d
test
in
g
s
ets.
T
h
e
tr
ain
in
g
s
et
c
o
n
tai
n
s
d
ata
u
p
to
a
ce
r
tain
p
o
in
t
(
all
d
ata
ex
c
ep
t
th
e
last
8
y
ea
r
s
)
,
wh
ile
t
h
e
test
in
g
s
et
co
n
tain
s
th
e
r
em
ain
in
g
d
ata
(
th
e
last
8
y
ea
r
s
)
.
iii)
Mo
d
el
tr
ain
in
g
:
a
n
XGBo
o
s
t
r
eg
r
ess
io
n
m
o
d
el
will b
e
in
itial
ized
an
d
f
itted
u
s
in
g
th
e
tr
ain
i
n
g
d
ata.
iv
)
Pre
d
ictio
n
:
t
h
e
m
o
d
el
p
r
e
d
icts
cr
u
d
e
o
il
p
r
ices
f
o
r
ea
ch
m
o
n
th
o
f
t
h
e
y
ea
r
s
2
0
1
5
to
2
0
2
2
.
I
t
iter
ates
th
r
o
u
g
h
ea
ch
y
ea
r
,
p
r
ed
icts
p
r
i
ce
s
f
o
r
ea
ch
m
o
n
th
o
f
th
at
y
ea
r
,
an
d
s
to
r
es th
e
p
r
ed
ictio
n
s
.
T
ab
le
1
.
Fo
r
ec
ast o
f
y
ea
r
s
2
0
1
5
-
2
0
2
2
f
o
r
th
e
d
ataset
C
r
u
d
e_
Oil_
Pric
e
b
y
u
s
in
g
th
e
XGBo
o
s
t m
o
d
el
Y
e
a
r
P
r
e
d
i
c
t
e
d
c
r
u
d
e
o
i
l
p
r
i
c
e
2
0
1
5
4
9
.
3
0
7
5
2
5
6
3
2
0
1
6
4
4
.
4
6
8
7
3
8
5
6
2
0
1
7
5
1
.
8
5
5
0
6
4
3
9
2
0
1
8
6
4
.
5
8
9
4
8
5
1
7
2
0
1
9
5
7
.
1
8
2
8
0
0
2
9
2
0
2
0
3
8
.
5
9
6
1
4
5
6
3
2
0
2
1
6
8
.
0
6
9
1
4
5
2
2
0
2
2
9
4
.
6
3
5
7
7
2
7
1
Fig
u
r
e
3
.
Fo
r
ec
ast o
f
y
ea
r
s
2
0
1
5
-
2
0
2
2
f
o
r
t
h
e
d
ataset
C
r
u
d
e
_
Oil_
Pric
e
b
y
u
s
in
g
t
h
e
XGBo
o
s
t m
o
d
el
2
.
3
.
2
.
Acc
ura
cy
ex
a
m
ina
t
io
n
R
MSE
an
d
MA
PE
wer
e
im
p
le
m
en
ted
to
ch
ec
k
th
e
lev
el
o
f
a
cc
u
r
ac
y
o
f
t
h
e
XGBo
o
s
t
m
o
d
el
in
ter
m
s
o
f
tim
e
s
er
ies.
T
h
e
r
esu
lts
wer
e
th
en
co
m
p
ar
ed
with
t
h
e
R
MSE
an
d
MA
PE
v
alu
es
o
f
th
e
p
r
o
p
o
s
e
d
hybr
id
-
AR
I
MA
-
E
M
p
r
esen
ted
in
s
ec
tio
n
2
.
2
.
B
o
th
m
o
d
els
wer
e
ev
alu
ated
u
s
in
g
th
e
s
am
e
d
ataset
an
d
p
er
io
d
,
as sh
o
wn
in
T
ab
le
2
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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N
:
2
2
5
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t J Ar
tif
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n
tell
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Vo
l.
15
,
No
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4
,
Au
g
u
s
t 2
0
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6
:
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1
3
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3
1
4
3
3136
T
ab
le
2
.
R
esu
lts
o
f
R
MSE
an
d
MA
PE
f
o
r
th
e
f
o
r
ec
asti
n
g
m
o
d
els XGBo
o
s
t a
n
d
h
y
b
r
id
-
AR
I
MA
-
EM
F
o
r
e
c
a
st
i
n
g
m
o
d
e
l
R
M
S
E
M
A
P
E
X
G
B
o
o
st
2
.
6
7
3
.
1
0
H
y
b
r
i
d
-
A
R
I
M
A
-
EM
1
.
0
4
0
.
0
0
9
2
.
4
.
G
a
t
ed
re
curr
ent
un
it
T
h
e
GR
U
-
b
ased
p
r
ed
ictio
n
m
o
d
el
aim
s
to
f
o
r
ec
ast
f
u
tu
r
e
p
o
in
ts
b
ased
o
n
p
r
e
v
io
u
s
d
ata
p
o
in
ts
[
1
9
]
–
[
2
1
]
.
I
t
will
b
e
ap
p
lied
to
p
r
e
d
ict
y
ea
r
s
2
0
1
0
-
2
0
2
3
f
o
r
th
e
d
ataset
C
r
u
d
e_
O
il_
Pric
e
,
as
s
ee
n
in
T
ab
le
3
an
d
Fig
u
r
es
4
a
n
d
5
.
T
h
e
s
tep
s
as
f
o
llo
ws
th
at
ar
e
n
ee
d
ed
to
d
em
o
n
s
tr
ate
an
d
s
h
o
r
tly
ex
p
lain
t
h
e
wh
o
le
p
r
o
g
r
ess
:
i)
Data
ex
tr
ac
tio
n
an
d
p
r
e
p
ar
a
tio
n
:
lo
ad
s
th
e
tar
g
eted
co
l
u
m
n
s
(
y
ea
r
s
,
o
il
p
r
ices
)
f
r
o
m
th
e
d
ataset
(
C
r
u
d
e_
Oil_
Pric
e)
.
ii)
No
r
m
aliza
tio
n
:
th
e
d
ata
is
n
o
r
m
alize
d
u
s
in
g
m
in
-
m
ax
s
ca
li
n
g
to
b
r
in
g
all
f
ea
t
u
r
es
to
th
e
s
am
e
s
ca
le,
ty
p
ically
b
etwe
en
0
an
d
1
.
iii)
T
r
ain
-
test
s
p
lit:
th
e
d
ataset
is
s
p
lit
8
0
:2
0
in
t
o
tr
ain
in
g
an
d
test
in
g
s
ets,
with
o
u
t
s
h
u
f
f
lin
g
to
p
r
eser
v
e
tem
p
o
r
al
o
r
d
er
.
iv
)
Data
r
esh
ap
in
g
:
th
e
in
p
u
t d
ata
is
r
esh
ap
ed
to
f
it th
e
i
n
p
u
t r
e
q
u
ir
em
en
ts
o
f
th
e
GR
U
m
o
d
el.
v)
Mo
d
el
b
u
ild
in
g
:
a
s
eq
u
e
n
tial
n
eu
r
al
n
etwo
r
k
m
o
d
el
is
co
n
s
tr
u
cted
u
s
in
g
Ker
as
with
th
e
A
d
am
o
p
tim
izer
an
d
m
ea
n
s
q
u
a
r
ed
er
r
o
r
(
MS
E
)
lo
s
s
f
u
n
ctio
n
.
I
t
c
o
n
s
is
ts
o
f
a
GR
U
lay
er
with
5
0
u
n
it
s
an
d
r
ec
tifie
d
lin
ea
r
u
n
it
(
R
eL
U
)
ac
tiv
atio
n
f
u
n
ctio
n
,
f
o
llo
wed
b
y
a
d
en
s
e
l
ay
er
with
o
n
e
u
n
it.
v
i)
Mo
d
el
tr
ain
in
g
:
t
h
e
m
o
d
el
is
tr
ain
ed
u
s
in
g
th
e
tr
ain
in
g
d
ata
f
o
r
5
0
ep
o
ch
s
with
a
b
at
ch
s
ize
o
f
3
2
.
Valid
atio
n
d
ata
is
p
r
o
v
id
ed
to
m
o
n
ito
r
th
e
m
o
d
el'
s
p
er
f
o
r
m
a
n
ce
d
u
r
i
n
g
tr
ain
i
n
g
.
v
ii)
Pre
d
ictio
n
:
th
e
tr
ain
ed
m
o
d
el
is
u
s
ed
t
o
m
a
k
e
p
r
ed
ictio
n
s
o
n
th
e
test
in
g
d
ata.
Pre
d
ictio
n
s
ar
e
i
n
v
er
s
e
-
tr
an
s
f
o
r
m
ed
to
o
b
tain
ac
tu
al
cr
u
d
e
o
il p
r
ices.
v
iii)
E
v
alu
atio
n
:
th
e
m
o
d
el'
s
p
er
f
o
r
m
an
ce
(
R
MSE
an
d
MA
PE
)
is
co
m
p
ar
e
d
with
h
y
b
r
id
-
A
R
I
MA
-
E
M
in
T
ab
le
4
.
T
o
co
n
clu
d
e,
Fig
u
r
e
6
s
h
o
ws
f
o
r
ec
asti
n
g
f
o
r
all
s
elec
ted
m
o
d
els
(
XGBo
o
s
t,
G
R
U
,
an
d
h
y
b
r
id
_
AR
I
MA
_
E
M
)
,
o
n
th
e
C
r
u
d
e_
Oil_
Pric
e
d
ataset
f
o
r
th
e
y
ea
r
s
2
0
1
5
-
2
0
2
2
.
T
ab
le
3
.
Fo
r
ec
ast o
f
y
ea
r
s
2
0
1
5
-
2
0
2
2
f
o
r
th
e
d
ataset
C
r
u
d
e_
Oil_
Pric
e
b
y
u
s
in
g
th
e
GR
U
m
o
d
el
Y
e
a
r
P
r
e
d
i
c
t
e
d
C
r
u
d
e
_
O
i
l
_
P
r
i
c
e
2
0
1
5
7
3
.
3
8
4
5
7
2
0
1
6
8
4
.
8
3
7
6
2
2
0
1
7
8
8
.
6
4
7
5
8
2
0
1
8
8
8
.
0
4
5
4
3
2
0
1
9
8
8
.
0
4
5
4
3
2
0
2
0
5
9
.
2
8
6
8
5
2
0
2
1
5
1
.
2
5
0
3
9
2
0
2
2
6
1
.
8
5
5
0
1
Fig
u
r
e
4
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el
to
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ii)
No
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r
ity
a
n
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tem
p
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n
d
s
:
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I
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I
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3139
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W
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.
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Evaluation Warning : The document was created with Spire.PDF for Python.