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k
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s
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term
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teg
y
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n
wo
rl
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su
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a
r
f
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tu
r
e
s
p
rice
s.
F
lu
c
tu
a
ti
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s
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su
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p
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h
a
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p
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s
b
e
c
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re
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f
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rm
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ter
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m
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v
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ried
c
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a
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n
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ffe
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ts.
F
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rt
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re
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t
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term
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term
p
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m
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in
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h
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g
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g
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a
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c
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ra
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y
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K
ey
w
o
r
d
s
:
Dir
ec
t
L
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n
g
s
h
o
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t
-
ter
m
m
e
m
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y
Mu
lti
-
in
p
u
t m
u
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o
u
tp
u
t
R
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s
iv
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Su
g
ar
T
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s
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p
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c
e
ss
a
rticle
u
n
d
e
r th
e
CC B
Y
-
SA
li
c
e
n
se
.
C
o
r
r
e
s
p
o
nd
ing
A
uth
o
r
:
W
an
d
ee
W
an
is
h
s
ak
p
o
n
g
Dep
ar
tm
en
t o
f
Statis
tics
,
Facu
lty
o
f
Scien
ce
s
,
Kasets
ar
t U
n
iv
er
s
ity
5
0
Ng
am
wo
n
g
wan
R
d
,
L
at
Ya
o
,
C
h
atu
ch
ak
,
B
an
g
k
o
k
,
T
h
ail
an
d
E
m
ail: w
an
d
ee
.
w@
k
u
.
th
1.
I
NT
RO
D
UCT
I
O
N
T
im
e
s
er
ies
d
ata
ar
e
f
o
r
m
ed
b
y
a
s
er
ies
o
f
o
b
s
er
v
atio
n
s
ar
r
an
g
ed
in
ac
co
r
d
an
ce
with
o
r
d
er
o
f
ev
en
ts
.
An
aly
s
is
o
f
tim
e
s
er
ie
s
d
ata
f
o
cu
s
es
o
n
d
ev
elo
p
i
n
g
s
to
ch
a
s
tic
an
d
d
y
n
am
ic
m
o
d
els
f
o
r
d
ata
d
ep
en
d
en
ce
,
ap
p
ly
in
g
th
em
to
v
a
r
io
u
s
im
p
o
r
tan
t
ar
ea
s
[
1
]
.
On
e
o
f
th
e
c
ap
ab
ilit
ies
o
f
tim
e
s
er
ie
s
an
al
y
s
is
i
s
f
o
r
ec
asti
n
g
,
wh
ich
allo
ws
u
s
to
p
r
ed
ict
f
u
tu
r
e
v
al
u
es
b
ased
o
n
p
ast
o
b
s
er
v
atio
n
s
.
M
o
n
tg
o
m
er
y
et
a
l
.
[
2
]
s
tate
th
at
th
is
f
o
r
ec
asti
n
g
is
cr
u
cial
as it p
r
o
v
id
es a
f
u
tu
r
e
p
er
s
p
ec
tiv
e,
ai
d
in
g
in
th
e
p
lan
n
i
n
g
an
d
d
ec
is
io
n
-
m
ak
in
g
p
r
o
ce
s
s
.
T
h
er
e
a
r
e
v
a
r
io
u
s
m
eth
o
d
s
th
at
ca
n
b
e
u
s
ed
f
o
r
f
o
r
ec
asti
n
g
,
r
an
g
in
g
f
r
o
m
class
ical
tech
n
iq
u
es
s
u
ch
as
a
u
to
r
eg
r
ess
iv
e
(
AR
)
,
m
o
v
i
n
g
av
er
a
g
e
(
MA
)
,
a
u
to
r
eg
r
ess
iv
e
in
teg
r
ated
m
o
v
in
g
av
er
a
g
e
(
AR
I
MA
)
to
d
ee
p
lear
n
in
g
m
o
d
els
lik
e
lo
n
g
s
h
o
r
t
-
ter
m
m
em
o
r
y
(
L
STM
)
.
L
STM
,
as
a
d
ee
p
lear
n
in
g
m
o
d
el,
is
ef
f
ec
tiv
e
in
ca
p
tu
r
in
g
an
d
u
n
d
er
s
tan
d
in
g
p
atter
n
s
f
r
o
m
s
eq
u
e
n
tial
d
ata.
Fu
r
th
er
m
o
r
e,
L
STM
is
a
b
as
ic
n
o
n
lin
ea
r
m
o
d
el
f
o
r
tim
e
s
er
ies
an
aly
s
is
th
at
c
an
co
m
p
r
e
h
en
d
t
h
e
n
o
n
-
lin
ea
r
n
atu
r
e
o
f
d
ata
[
3
]
.
A
r
ea
l
-
w
o
r
ld
ap
p
licatio
n
o
f
L
STM
is
in
f
o
r
ec
asti
n
g
g
lo
b
al
s
u
g
ar
f
u
tu
r
es p
r
ices u
s
in
g
a
m
u
lti
-
s
tep
ah
ea
d
f
o
r
ec
asti
n
g
s
tr
ateg
y
.
T
h
is
s
tr
ateg
y
ca
n
p
r
ed
ict
v
alu
es
f
o
r
s
ev
e
r
al
f
u
tu
r
e
p
er
io
d
s
with
v
a
r
io
u
s
t
y
p
es
o
f
s
tr
ateg
ies,
n
am
ely
r
e
cu
r
s
iv
e,
d
ir
ec
t,
a
n
d
m
u
lti
-
in
p
u
t m
u
lti
-
o
u
tp
u
t
(
MI
MO
)
.
His
to
r
ically
,
s
u
g
ar
h
as
b
ee
n
o
n
e
o
f
th
e
m
o
s
t
v
o
latile
co
m
m
o
d
ities
[
4
]
.
Flu
ctu
atio
n
s
in
s
u
g
ar
p
r
ices
im
p
ac
t
v
ar
io
u
s
s
ec
to
r
s
,
in
clu
d
i
n
g
ag
r
icu
ltu
r
e,
tr
ad
e
,
an
d
in
d
u
s
tr
y
,
p
ar
ticu
lar
ly
th
e
f
o
o
d
an
d
b
ev
er
ag
e
in
d
u
s
tr
y
.
Acc
o
r
d
in
g
to
Ha
n
an
i
et
a
l.
[
5
]
,
an
in
cr
ea
s
e
in
s
u
g
ar
p
r
ices
will
p
r
o
m
p
t
s
u
g
ar
ca
n
e
f
ar
m
er
s
to
ex
p
a
n
d
th
e
a
r
ea
Evaluation Warning : The document was created with Spire.PDF for Python.
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f
s
u
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ar
ca
n
e
p
lan
tatio
n
s
,
ca
u
s
in
g
a
r
ed
u
ctio
n
in
th
e
p
r
o
d
u
ctio
n
o
f
o
t
h
er
cr
o
p
s
an
d
ag
r
icu
ltu
r
al
p
r
o
d
u
cts.
Mo
r
eo
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ea
s
ier
m
ar
k
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ac
c
ess
ca
n
lead
to
a
d
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ea
s
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n
d
o
m
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c
s
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a
r
p
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o
d
u
ctio
n
an
d
a
n
in
cr
ea
s
e
i
n
im
p
o
r
ts
,
tr
ig
g
er
in
g
h
ig
h
ex
p
o
r
t
lev
els
f
r
o
m
ex
p
o
r
tin
g
co
u
n
tr
ies
s
u
ch
as
B
r
az
il
an
d
u
ltima
tely
r
aisi
n
g
g
lo
b
al
s
u
g
ar
p
r
ices
[
6
]
.
T
h
e
r
is
e
in
s
u
g
ar
p
r
ices
will
also
in
cr
ea
s
e
p
r
o
d
u
ctio
n
c
o
s
ts
,
ca
u
s
in
g
th
e
f
o
o
d
an
d
b
ev
er
a
g
e
in
d
u
s
tr
y
to
r
e
d
u
ce
p
r
o
d
u
ctio
n
lev
els
[
5
]
.
Fu
tu
r
es
co
n
tr
ac
ts
s
er
v
e
as
cr
u
cial
in
s
tr
u
m
en
ts
u
s
ed
b
y
tr
ad
er
s
an
d
in
v
esto
r
s
to
m
an
ag
e
an
d
h
ed
g
e
ag
ain
s
t
v
ar
io
u
s
r
is
k
s
in
th
e
f
in
an
cial
m
ar
k
ets
[
7
]
.
B
y
ap
p
l
y
in
g
L
STM
with
a
m
u
lti
-
s
tep
ah
ea
d
f
o
r
ec
asti
n
g
s
tr
ateg
y
,
f
o
r
ec
asti
n
g
s
u
g
a
r
f
u
tu
r
es
p
r
ices
is
ex
p
ec
ted
to
b
e
co
m
e
an
im
p
o
r
tan
t
to
o
l f
o
r
m
ar
k
et
p
ar
ticip
an
ts
to
an
ticip
ate
ch
an
g
es a
n
d
m
ak
e
in
f
o
r
m
e
d
d
ec
is
io
n
s
.
R
esear
ch
r
elate
d
to
s
u
g
ar
p
r
ice
f
o
r
ec
asti
n
g
h
as
b
ee
n
co
n
d
u
cted
b
y
Fau
ziah
an
d
Gu
n
ar
y
ati
[
8
]
,
co
m
p
ar
in
g
th
e
d
o
u
b
le
ex
p
o
n
en
tial
s
m
o
o
th
in
g
(
DE
S)
an
d
ar
tific
ial
n
eu
r
al
n
etwo
r
k
(
ANN)
m
o
d
els
in
f
o
r
ec
asti
n
g
d
aily
s
u
g
a
r
p
r
ices
in
Dep
o
k
.
T
h
e
r
esu
lts
o
f
th
is
s
tu
d
y
in
d
icate
th
at
ANN
h
as
b
etter
p
er
f
o
r
m
a
n
ce
.
An
o
th
er
s
tu
d
y
c
o
n
d
u
cted
b
y
Yu
r
ts
ev
er
[
9
]
c
o
m
p
ar
ed
d
ee
p
l
ea
r
n
in
g
m
o
d
els,
n
am
ely
L
ST
M,
b
id
ir
ec
tio
n
al
lo
n
g
s
h
o
r
t
-
ter
m
m
em
o
r
y
(
Bi
-
L
STM
)
,
an
d
g
ate
r
ec
u
r
r
en
t
u
n
it
(
G
R
U)
,
f
in
d
in
g
th
at
th
e
L
STM
m
o
d
el
p
er
f
o
r
m
ed
b
est
with
r
o
o
t
m
ea
n
s
q
u
a
r
e
e
r
r
o
r
(
R
MSE
)
v
alu
es
o
f
6
1
.
7
2
8
,
m
ea
n
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
o
f
4
8
.
8
5
,
an
d
m
ea
n
ab
s
o
lu
te
p
er
ce
n
tag
e
e
r
r
o
r
(
M
APE)
o
f
3
.
4
8
%.
T
h
is
s
tu
d
y
al
s
o
s
h
o
wed
th
at
ec
o
n
o
m
ic
in
d
i
ca
to
r
s
in
f
lu
en
ce
g
o
ld
p
r
ices.
I
n
ad
d
itio
n
t
o
r
esear
ch
co
m
p
ar
in
g
m
o
d
els,
th
e
r
e
is
also
r
esear
ch
b
y
Fer
r
e
i
r
a
an
d
C
u
n
h
a
[
1
0
]
co
m
p
ar
in
g
r
ec
u
r
s
iv
e,
d
ir
ec
t,
an
d
MI
MO
s
tr
ateg
ies
in
f
o
r
e
ca
s
tin
g
d
aily
r
ef
er
en
ce
e
v
ap
o
tr
an
s
p
ir
atio
n
u
s
in
g
d
ee
p
lear
n
in
g
.
T
h
e
r
esu
lts
in
d
i
ca
te
th
at
th
e
MI
MO
s
tr
ateg
y
i
s
th
e
b
est
s
tr
ateg
y
f
o
r
o
b
tain
in
g
th
e
m
o
s
t
ac
c
u
r
ate
f
o
r
ec
asts
.
T
h
e
o
b
jectiv
es
o
f
th
is
r
esear
ch
ar
e
to
id
e
n
tify
t
h
e
h
y
p
er
p
ar
am
eter
co
m
b
i
n
atio
n
s
th
at
y
ield
t
h
e
b
est
m
o
d
elin
g
p
er
f
o
r
m
an
ce
,
id
en
ti
f
y
th
e
m
u
lti
-
s
tep
ah
e
ad
f
o
r
ec
a
s
tin
g
s
tr
ateg
y
th
at
p
r
o
v
id
es
th
e
b
est
f
o
r
ec
asts
f
o
r
wo
r
ld
s
u
g
ar
f
u
tu
r
es p
r
ices,
an
d
f
o
r
ec
ast wo
r
ld
s
u
g
ar
f
u
tu
r
es
p
r
ices u
s
in
g
th
e
b
est m
o
d
el.
2.
M
E
T
H
O
D
2
.
1
.
Da
t
a
T
h
e
d
ata
u
s
ed
in
th
is
r
esear
ch
co
n
s
is
ts
o
f
d
aily
p
r
ices
f
r
o
m
o
n
e
o
f
t
h
e
wo
r
ld
s
u
g
ar
f
u
tu
r
es
co
n
tr
ac
ts
,
s
p
ec
if
ically
th
e
I
C
E
NY
s
u
g
ar
#
1
1
f
u
tu
r
es
(
SB
c3
)
.
T
h
is
co
n
tact
s
er
v
es
as
a
p
r
im
a
r
y
b
en
ch
m
ar
k
f
o
r
r
aw
s
u
g
ar
d
er
iv
ed
f
r
o
m
s
u
g
ar
ca
n
e
an
d
en
ab
les
tr
ad
in
g
at
a
p
r
ed
et
er
m
in
ed
f
u
tu
r
e
p
r
ice.
T
h
e
“c
3
”
in
SB
c3
s
ig
n
if
ies
th
at
it
is
th
e
th
ir
d
co
n
tr
ac
t
av
ailab
le
in
s
eq
u
en
ce
f
o
r
f
u
tu
r
e
d
eliv
er
y
.
Data
was
s
o
u
r
ce
d
f
r
o
m
I
n
v
esti
n
g
.
co
m
at
h
ttp
://www.
in
v
esti
n
g
.
co
m
/co
m
m
o
d
ities
/u
s
-
s
u
g
ar
-
n
o
1
1
-
h
id
to
r
ical
-
d
ata?
ci
d
=1
1
8
6
9
6
5
,
c
o
v
er
in
g
th
e
o
b
s
er
v
atio
n
p
er
io
d
f
r
o
m
J
an
u
ar
y
2
,
2
0
1
9
,
to
Dec
em
b
e
r
2
9
,
2
0
2
3
,
with
a
to
tal
o
f
1
,
2
5
8
o
b
s
er
v
atio
n
s
.
T
h
e
u
n
i
t
u
s
ed
in
th
e
p
r
ices o
f
th
is
f
u
t
u
r
e
co
n
tr
ac
t is ce
n
ts
p
er
p
o
u
n
d
.
2
.
2
.
L
o
ng
s
ho
rt
-
t
er
m
m
emo
ry
L
STM
is
a
d
ee
p
lear
n
in
g
m
eth
o
d
d
e
v
elo
p
ed
f
r
o
m
r
ec
u
r
r
en
t
n
eu
r
al
n
etwo
r
k
s
(
R
NN)
ca
p
ab
le
o
f
lear
n
in
g
lo
n
g
-
ter
m
d
e
p
en
d
e
n
c
ies
an
d
r
etain
in
g
in
f
o
r
m
atio
n
o
v
er
e
x
ten
d
ed
p
er
io
d
s
[
1
1
]
.
On
e
o
f
th
e
p
r
im
a
r
y
is
s
u
es
th
at
L
STM
ad
d
r
ess
es
i
s
th
e
v
an
is
h
in
g
g
r
ad
ien
t
p
r
o
b
l
em
in
R
NNs.
T
h
i
s
p
r
o
b
lem
m
ak
es
it
d
if
f
icu
lt
f
o
r
R
NNs
to
lear
n
lo
n
g
-
ter
m
r
elatio
n
s
h
ip
s
in
d
ata
b
ec
a
u
s
e
th
e
g
r
ad
ien
ts
o
f
th
e
e
r
r
o
r
f
u
n
ctio
n
t
en
d
to
b
ec
o
m
e
v
e
r
y
s
m
all,
ca
u
s
in
g
th
e
lear
n
in
g
p
r
o
ce
s
s
to
h
alt
[
1
2
]
.
L
STM
h
as a
s
tr
u
ctu
r
e
th
at
ca
n
s
elec
tiv
ely
r
em
em
b
e
r
o
r
f
o
r
g
e
t
in
f
o
r
m
atio
n
th
r
o
u
g
h
its
ce
ll
s
tate
an
d
th
r
ee
g
ates
[
1
1
]
.
T
h
e
s
tr
u
ctu
r
e
o
f
an
L
STM
c
o
n
s
is
ts
o
f
f
o
u
r
m
ain
co
m
p
o
n
en
ts
th
at
in
ter
ac
t a
t e
a
ch
tim
e
s
tep
:
i)
C
ell
s
tate
(
)
:
th
e
ce
ll
s
tate
is
th
e
m
ain
co
m
p
o
n
en
t
in
an
L
STM
,
f
u
n
ctio
n
in
g
as
lo
n
g
-
ter
m
m
em
o
r
y
[
1
3
]
.
T
h
e
p
r
o
ce
s
s
f
o
r
th
e
ce
ll
s
tate
r
esem
b
les
a
co
n
v
ey
o
r
b
elt,
wh
er
e
p
ar
am
eter
i
n
f
o
r
m
atio
n
m
o
v
es
lin
ea
r
ly
with
in
ter
ac
tio
n
s
s
u
ch
as
m
u
l
tip
licatio
n
an
d
ad
d
itio
n
.
T
h
e
s
tatu
s
o
f
th
e
in
f
o
r
m
atio
n
d
e
p
en
d
s
o
n
th
ese
in
ter
ac
tio
n
s
,
an
d
if
th
er
e
is
n
o
in
ter
ac
tio
n
,
th
e
i
n
f
o
r
m
atio
n
r
e
m
ain
s
u
n
ch
an
g
ed
[
1
4
]
.
ii)
Fo
r
g
et
g
ate
(
)
:
th
e
f
o
r
g
et
g
ate
d
eter
m
in
es
wh
ich
in
f
o
r
m
atio
n
s
h
o
u
ld
b
e
d
is
ca
r
d
ed
o
r
r
etain
ed
f
r
o
m
th
e
ce
ll
s
tate.
T
h
e
s
ig
m
o
id
ac
tiv
at
io
n
f
u
n
ctio
n
(
σ
)
is
u
s
ed
at
th
i
s
s
tag
e,
p
r
o
d
u
cin
g
v
alu
es
b
etwe
en
0
a
n
d
1
.
A
v
alu
e
o
f
0
m
ea
n
s
th
e
in
f
o
r
m
atio
n
will
b
e
d
is
ca
r
d
ed
,
wh
il
e
a
v
al
u
e
o
f
1
m
ea
n
s
th
e
i
n
f
o
r
m
atio
n
will
b
e
r
etain
ed
[
1
4
]
.
iii)
I
n
p
u
t
g
ate
(
)
:
th
e
in
p
u
t
g
ate
c
o
n
tr
o
ls
th
e
in
f
o
r
m
atio
n
th
at
w
ill
b
e
ad
d
ed
to
th
e
ce
ll
s
tate
f
r
o
m
th
e
latest
in
p
u
t
v
alu
e
(
)
an
d
p
r
o
tects
m
e
m
o
r
y
f
r
o
m
i
r
r
elev
an
t
i
n
p
u
t.
T
h
er
e
ar
e
two
la
y
er
s
th
at
d
eter
m
in
e
th
e
n
ew
m
em
o
r
y
s
to
r
ed
in
t
h
e
ce
ll
s
tate:
th
e
s
ig
m
o
id
lay
er
an
d
th
e
tan
h
lay
er
.
T
h
e
s
ig
m
o
id
lay
er
d
ec
id
es
th
e
u
p
d
ated
v
alu
es,
wh
ile
th
e
tan
h
lay
er
f
o
r
m
s
a
v
ec
to
r
o
f
n
ew
c
an
d
id
ate
v
alu
es f
o
r
th
e
ce
ll st
a
te
(
̃
)
[
1
4
]
.
iv
)
Ou
tp
u
t
g
ate
(
)
:
th
e
o
u
tp
u
t
g
at
e
co
n
tr
o
ls
th
e
in
f
o
r
m
atio
n
co
n
tain
ed
in
th
e
u
p
d
ate
d
ce
ll
s
tate
(
)
th
at
will
b
e
s
en
t
to
th
e
o
u
tp
u
t
at
ea
ch
tim
e
s
tep
.
T
h
is
g
ate
d
eter
m
in
es
th
e
v
alu
e
o
f
t
h
e
n
ex
t h
id
d
en
s
tate
b
ased
o
n
th
e
p
r
ev
i
o
u
s
h
id
d
en
s
tate
(
ℎ
−
1
)
,
th
e
cu
r
r
en
t
in
p
u
t,
a
n
d
th
e
n
ewly
u
p
d
ated
ce
ll
s
tate
[
1
4
]
.
T
h
is
o
p
tim
izatio
n
m
eth
o
d
co
m
b
in
e
s
tech
n
iq
u
es
f
r
o
m
o
th
e
r
o
p
ti
m
izatio
n
m
eth
o
d
s
s
u
ch
as
a
d
ap
tiv
e
g
r
ad
ien
t
(
Ad
aGr
ad
)
,
w
h
ich
wo
r
k
s
well
with
s
p
ar
s
e
g
r
ad
ien
ts
an
d
r
o
o
t
m
ea
n
s
q
u
ar
e
p
r
o
p
ag
atio
n
(
R
MSp
r
o
p
)
[
1
5
]
.
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
F
o
r
ec
a
s
tin
g
w
o
r
ld
s
u
g
a
r
co
n
t
r
a
ct
fu
tu
r
es u
s
in
g
lo
n
g
s
h
o
r
t
-
t
erm m
emo
r
y
…
(
K
h
a
ir
il A
n
w
a
r
N
o
to
d
ip
u
tr
o
)
2635
2
.
3
.
M
ulti
-
s
t
ep
a
hea
d t
im
e
s
er
ies f
o
re
ca
s
t
ing
s
t
ra
t
eg
y
Mu
lti
-
s
tep
ah
ea
d
tim
e
s
er
ies
f
o
r
ec
asti
n
g
aim
s
to
p
r
ed
ict
th
e
v
alu
es
f
o
r
th
e
n
ex
t
tim
e
p
er
io
d
s
[
,
.
.
.
,
+
]
b
ased
o
n
ex
is
tin
g
h
is
to
r
ical
ti
m
e
s
er
ies
d
ata
[
1
6
]
.
T
h
e
f
o
llo
win
g
ar
e
s
tr
ateg
ies
ap
p
lied
to
o
b
tain
f
o
r
ec
asts
f
o
r
s
ev
er
al
f
u
tu
r
e
p
er
io
d
s
.
2
.
3
.
1
.
Rec
urs
iv
e
s
t
ra
t
eg
y
T
h
e
r
ec
u
r
s
iv
e
s
tr
ateg
y
is
th
e
s
im
p
lest
ap
p
r
o
ac
h
to
p
r
ed
ictin
g
v
alu
es
f
o
r
m
u
ltip
le
f
u
tu
r
e
tim
e
p
er
io
d
s
[
1
6
]
.
T
h
e
p
r
in
ci
p
le
o
f
th
is
s
tr
ateg
y
is
to
u
s
e
th
e
f
o
r
ec
asted
r
esu
lt
as
an
in
p
u
t
to
g
en
er
ate
th
e
p
r
ed
ictio
n
f
o
r
th
e
n
ex
t d
a
y
[
1
6
]
.
̂
+
ℎ
=
{
̂
(
,
…
,
−
+
1
)
,
ℎ
=
1
̂
(
̂
+
ℎ
−
1
,
…
,
̂
+
1
,
̂
,
…
,
−
+
1
)
,
ℎ
∈
{
2
,
…
,
}
̂
(
̂
+
ℎ
−
1
,
…
,
̂
−
+
1
)
,
ℎ
∈
{
+
1
,
…
,
}
(
1
)
W
h
er
e
is
i
n
d
ex
o
f
th
e
cu
r
r
e
n
t
tim
e
p
er
io
d
,
ℎ
is
p
r
ed
icted
tim
e
p
er
io
d
,
is
n
u
m
b
er
o
f
p
r
ev
io
u
s
tim
e
p
er
io
d
s
u
s
ed
as
in
p
u
t
t
o
m
a
k
e
t
h
e
p
r
ed
ictio
n
,
is
n
u
m
b
er
o
f
p
r
ed
i
cted
tim
e
p
er
io
d
s
,
an
d
̂
(
)
is
m
o
d
el
u
s
ed
f
o
r
f
o
r
ec
asti
n
g
.
2
.
3
.
2
.
Dire
ct
s
t
ra
t
eg
y
T
h
is
s
tr
ateg
y
d
o
es
n
o
t
u
s
e
p
r
ev
io
u
s
f
o
r
ec
ast
r
esu
lts
as
in
p
u
ts
.
I
n
s
tead
,
ea
ch
f
o
r
ec
ast
r
esu
lt
h
as
its
o
wn
m
o
d
el
[
1
6
]
.
As
a
r
esu
lt,
th
e
er
r
o
r
in
o
n
e
f
o
r
ec
ast
v
alu
e
d
o
es
n
o
t
ac
c
u
m
u
late
in
to
t
h
e
f
o
r
ec
ast
v
alu
e
f
o
r
th
e
s
u
b
s
eq
u
en
t p
er
io
d
[
1
7
]
.
̂
+
ℎ
=
̂
ℎ
(
,
…
,
−
+
1
)
(
2
)
W
h
er
e
is
i
n
d
ex
o
f
th
e
cu
r
r
e
n
t
tim
e
p
er
io
d
,
ℎ
is
p
r
ed
icted
tim
e
p
er
io
d
,
is
n
u
m
b
er
o
f
p
r
ev
io
u
s
tim
e
p
er
io
d
s
u
s
ed
as in
p
u
t to
m
ak
e
th
e
p
r
ed
ictio
n
,
an
d
ℎ
̂
(
)
is
t
h
e
m
o
d
el
u
s
ed
t
o
f
o
r
ec
ast th
e
h
-
th
p
er
io
d
.
2
.
3
.
3
.
M
ulti
-
inp
ut
m
ulti
-
o
utput
T
h
is
s
tr
ateg
y
g
en
er
ates
f
o
r
ec
ast
v
alu
es
f
o
r
s
ev
er
al
f
u
tu
r
e
p
er
io
d
s
s
im
u
ltan
eo
u
s
ly
b
y
u
s
in
g
a
m
o
d
el
th
at
tak
es in
to
ac
co
u
n
t sev
er
al
in
p
u
ts
at
o
n
ce
[
1
8
]
.
[
̂
+
,
…
,
̂
+
1
]
=
̂
(
,
…
,
−
+
1
)
(
3
)
W
h
er
e
is
i
n
d
ex
o
f
th
e
cu
r
r
e
n
t
tim
e
p
er
io
d
,
is
n
u
m
b
er
o
f
p
r
ev
io
u
s
tim
e
p
er
io
d
s
u
s
ed
as
in
p
u
t
to
m
ak
e
th
e
p
r
ed
ictio
n
,
is
n
u
m
b
e
r
o
f
p
r
ed
i
cted
tim
e
p
er
io
d
s
,
a
n
d
̂
(
)
is
m
o
d
el
u
s
ed
f
o
r
f
o
r
ec
asti
n
g
.
2
.
4
.
Ana
ly
s
is
p
ro
ce
du
re
Data
an
aly
s
is
wa
s
co
n
d
u
cted
u
s
in
g
Py
th
o
n
s
o
f
twar
e.
Py
th
o
n
is
a
p
o
p
u
lar
s
o
f
twar
e
f
o
r
s
tatis
tics
an
d
d
ata
s
cien
ce
r
esear
ch
.
Usi
n
g
th
e
s
o
f
twar
e
an
d
th
e
th
e
o
r
etica
l
f
r
am
ewo
r
k
th
e
p
r
o
ce
d
u
r
al
s
t
ep
s
f
o
r
th
e
an
aly
s
is
in
th
is
r
esear
ch
ar
e
as f
o
llo
ws
:
i)
Data
ex
p
lo
r
atio
n
to
d
ete
r
m
in
e
th
e
d
ata
ch
ar
ac
ter
is
tics
,
tr
en
d
s
,
s
ea
s
o
n
al
p
atter
n
s
,
tr
en
d
c
h
an
g
e
p
atter
n
s
o
v
er
5
y
ea
r
s
,
an
d
s
tatio
n
ar
ity
d
ata.
ii)
Sp
litt
in
g
th
e
d
ata
in
to
tr
ai
n
in
g
d
ata
(
8
0
%)
a
n
d
test
d
ata
(
2
0
%).
iii)
No
r
m
alizin
g
th
e
d
ata
u
s
in
g
t
h
e
m
in
-
m
ax
n
o
r
m
aliza
tio
n
m
eth
o
d
.
N
o
r
m
aliza
tio
n
is
n
ec
e
s
s
ar
y
ev
en
f
o
r
u
n
iv
ar
iate
d
ata
b
ec
a
u
s
e
ac
co
r
d
in
g
to
L
i
a
n
d
C
ao
[
1
9
]
,
L
S
T
M
u
s
in
g
s
ig
m
o
i
d
an
d
tan
h
as
ac
tiv
atio
n
f
u
n
ctio
n
s
ar
e
s
en
s
itiv
e
to
th
e
in
p
u
t d
ata
r
an
g
e.
=
−
−
(
4
)
iv
)
Ad
ju
s
tin
g
th
e
d
ata
d
im
e
n
s
io
n
s
h
ap
e
ac
co
r
d
i
n
g
to
t
h
e
ap
p
r
o
a
ch
u
s
ed
.
‒
Sin
g
le
-
o
u
tp
u
t:
t
h
e
d
ata
d
im
en
s
io
n
f
o
r
th
e
L
STM
m
o
d
el
in
th
is
ap
p
r
o
ac
h
will
b
e
a
r
r
an
g
e
d
in
th
e
f
o
r
m
o
f
(
n
u
m
b
e
r
o
f
s
am
p
les,
n
u
m
b
er
o
f
tim
e
s
tep
s
,
n
u
m
b
e
r
o
f
v
a
r
iab
les).
T
h
e
r
ec
u
r
s
iv
e
a
n
d
d
ir
ec
t
s
tr
ateg
ies will u
s
e
m
o
d
els f
r
o
m
L
STM
tr
ain
in
g
r
esu
lts
with
a
s
in
g
le
-
o
u
tp
u
t a
p
p
r
o
ac
h
.
‒
Mu
lti
-
o
u
tp
u
t:
t
h
e
d
ata
d
im
e
n
s
io
n
f
o
r
th
e
L
STM
m
o
d
el
in
th
i
s
s
tr
ateg
y
will
b
e
ar
r
an
g
ed
i
n
t
h
e
f
o
r
m
o
f
(
n
u
m
b
er
o
f
s
am
p
les,
n
u
m
b
er
o
f
tim
e
s
tep
s
,
an
d
n
u
m
b
er
o
f
in
p
u
t
v
ar
iab
les)
f
o
r
in
p
u
t
an
d
(
n
u
m
b
e
r
o
f
s
am
p
les,
n
u
m
b
er
o
f
f
u
tu
r
e
tim
e
s
tep
s
,
an
d
n
u
m
b
er
o
f
o
u
tp
u
t
v
a
r
iab
les)
f
o
r
o
u
tp
u
t.
T
h
e
MI
MO
s
tr
ateg
y
will u
s
e
m
o
d
e
ls
f
r
o
m
L
STM
tr
ain
in
g
r
esu
lts
with
a
m
u
lti
-
o
u
tp
u
t a
p
p
r
o
ac
h
.
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.
1
5
,
No
.
3
,
J
u
n
e
2
0
2
6
:
2
6
3
3
-
2
6
4
2
2636
v)
Mo
d
elin
g
with
L
STM
.
‒
C
r
ea
tin
g
k
-
f
o
ld
tim
e
s
er
ies
cr
o
s
s
-
v
alid
atio
n
(
C
V)
s
ce
n
ar
i
o
s
b
y
d
iv
id
in
g
th
e
tr
ain
in
g
d
ata
in
t
o
tr
ain
in
g
an
d
v
alid
atio
n
d
ata
f
o
r
ea
ch
f
o
ld
wh
ile
s
till
co
n
s
id
er
in
g
th
e
tim
e
o
r
d
er
.
‒
Ap
p
ly
in
g
th
e
L
STM
m
eth
o
d
t
o
ea
ch
f
o
ld
f
o
r
ea
c
h
co
m
b
in
at
io
n
o
f
h
y
p
er
p
ar
am
eter
s
u
s
ed
a
s
s
h
o
wn
in
T
ab
le
1
.
‒
T
r
ain
in
g
th
e
L
STM
m
o
d
el
with
th
e
in
itialized
h
y
p
er
p
ar
am
e
ter
co
m
b
in
atio
n
s
o
n
th
e
1
s
t
to
th
e
k
-
t
h
f
o
ld
.
‒
C
alcu
latin
g
th
e
av
er
ag
e
R
MSE
v
alu
e
f
r
o
m
t
h
e
v
alid
atio
n
d
ata
f
o
r
ea
ch
co
m
b
i
n
atio
n
o
f
h
y
p
er
p
ar
am
eter
-
tr
ai
n
ed
m
o
d
el
s
.
‒
R
ep
ea
tin
g
s
tep
s
c
an
d
d
with
d
if
f
er
en
t h
y
p
er
p
ar
am
eter
c
o
m
b
i
n
atio
n
s
.
‒
Selectin
g
th
e
co
m
b
in
atio
n
o
f
h
y
p
er
p
a
r
am
eter
s
with
th
e
s
m
allest av
er
ag
e.
‒
T
r
ain
in
g
th
e
L
STM
m
o
d
el
u
s
in
g
all
tr
ain
in
g
d
ata
with
th
e
b
e
s
t h
y
p
er
p
ar
a
m
eter
co
m
b
in
atio
n
.
v
i)
R
ep
ea
tin
g
s
tep
5
as m
an
y
tim
e
s
as th
e
len
g
th
o
f
d
ata
to
b
e
f
o
r
ec
asted
f
o
r
th
e
s
in
g
le
-
o
u
t
p
u
t
ap
p
r
o
ac
h
.
v
ii)
Den
o
r
m
alizin
g
th
e
d
ata
to
r
etu
r
n
to
th
e
o
r
ig
in
al
d
ata
s
ca
le.
v
iii)
E
v
alu
atin
g
th
e
m
o
d
el
o
n
th
e
test
d
ata
b
y
ap
p
l
y
in
g
th
e
m
u
lti
-
s
tep
ah
ea
d
f
o
r
ec
asti
n
g
s
tr
ateg
y
.
ix
)
Selectin
g
th
e
b
est s
tr
ateg
y
in
f
o
r
ec
asti
n
g
s
u
g
ar
f
u
tu
r
es p
r
ices u
s
in
g
R
MSE
,
MA
E
,
an
d
MA
PE
m
etr
ics.
x)
Selectin
g
th
e
s
tr
ateg
y
with
th
e
b
est m
o
d
el
m
etr
ic
v
alu
e.
x
i)
Fo
r
ec
asti
n
g
wo
r
ld
s
u
g
a
r
f
u
t
u
r
es c
o
n
tr
ac
t p
r
ices w
ith
th
e
b
es
t m
o
d
el
an
d
in
ter
p
r
etin
g
th
e
r
e
s
u
lts
.
T
ab
le
1
.
Hy
p
er
p
ar
a
m
eter
co
m
b
in
atio
n
H
y
p
e
r
p
a
r
a
me
t
e
r
H
i
d
d
e
n
l
a
y
e
r
Le
a
r
n
i
n
g
r
a
t
e
N
e
u
r
o
n
Ti
me
st
e
p
1
,
2
0
.
0
0
1
;
0
.
01
3
2
,
6
4
,
1
2
8
5
,
2
2
,
6
6
,
1
2
5
Acc
o
r
d
in
g
to
Sh
c
h
er
b
ak
o
v
et
a
l
.
[
2
0
]
,
R
MSE
an
d
MA
E
ar
e
er
r
o
r
m
ea
s
u
r
es
th
at
ca
n
b
e
u
s
ed
to
ev
alu
ate
th
e
ac
cu
r
ac
y
o
f
f
o
r
ec
asti
n
g
m
o
d
els
f
o
r
tim
e
s
er
ies
d
ata.
T
h
e
n
,
MA
PE
is
also
o
n
e
o
f
th
e
c
o
m
m
o
n
ly
u
s
ed
er
r
o
r
m
ea
s
u
r
es b
ec
au
s
e
it
is
n
o
t d
ep
en
d
en
t o
n
th
e
d
ata
s
ca
le
an
d
ea
s
y
to
in
te
r
p
r
et
[
2
1
]
.
=
√
1
∑
(
−
)
2
=
1
(
5
)
=
1
∑
|
−
|
=
1
(
6
)
=
1
∑
|
−
|
=
1
×
100
(
7
)
W
h
er
e
is
l
en
g
th
o
f
d
ata
,
is
a
ctu
al
v
alu
e
,
an
d
is
p
r
ed
icted
v
a
lu
e
.
3.
RE
SU
L
T
S AN
D
D
I
SCU
SS
I
O
N
3
.
1
.
Da
t
a
e
x
plo
ra
t
io
n
Ov
er
th
e
co
u
r
s
e
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s
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g
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Sep
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Fig
u
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1
s
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ain
.
Evaluation Warning : The document was created with Spire.PDF for Python.
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2252
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8
9
3
8
F
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co
n
t
r
a
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fu
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t
erm m
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(
K
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)
2637
Acc
o
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d
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g
to
Nu
r
h
a
m
b
ali
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t
a
l.
[
2
2
]
,
d
ata
th
at
ar
e
n
o
t
s
p
r
ea
d
ar
o
u
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th
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3
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allest
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r
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2
3
]
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Acc
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[
2
4
]
,
th
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w
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t
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a
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t
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t
r
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l
t
h
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e
f
f
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c
t
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c
a
p
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c
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t
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e
m
o
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i
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a
m
o
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c
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m
p
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x
w
a
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t
h
a
n
o
t
h
e
r
h
y
p
e
r
p
a
r
a
m
e
t
e
r
s
[
2
5
]
.
T
h
e
ti
m
e
s
te
p
c
a
n
d
e
t
e
r
m
i
n
e
t
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n
g
t
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t
h
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p
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v
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m
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p
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t
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p
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f
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t
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t
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r
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t
p
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t
h
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s
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f
f
ec
t
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g
t
h
e
m
o
d
e
l
'
s
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p
l
e
x
it
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.
Af
ter
d
eter
m
in
in
g
th
e
in
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o
f
h
y
p
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p
ar
am
eter
s
,
CV
is
p
er
f
o
r
m
ed
with
k
-
f
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l
d
s
p
ec
if
ic
to
tim
e
s
er
ies
d
ata
[
2
6
]
.
CV
is
co
n
d
u
cted
to
m
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s
u
r
e
m
o
d
el
p
e
r
f
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ce
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b
tai
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th
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t
o
p
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t
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m
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in
atio
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o
f
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p
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m
eter
s
,
an
d
d
etec
t
o
v
e
r
f
itti
n
g
.
T
h
e
v
alu
e
o
f
k
u
s
ed
is
6
with
s
eq
u
en
tial
tim
e
-
b
ase
d
d
ata
s
p
litt
in
g
as
s
h
o
wn
in
Fig
u
r
e
2
.
T
h
e
c
h
o
ice
o
f
k
=6
was
m
ad
e
to
en
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u
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t
h
a
t
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ch
f
o
l
d
co
v
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ap
p
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x
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ately
5
-
6
m
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n
th
s
o
f
d
ata
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o
r
b
o
th
tr
ain
i
n
g
an
d
v
alid
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n
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n
th
e
f
ir
s
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C
V
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e
m
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5
-
6
m
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alid
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th
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llo
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5
-
6
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n
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u
b
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th
e
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ata
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6
m
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ile
th
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a
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if
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R
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if
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e
f
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s
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ar
p
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r
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is
is
d
u
e
to
th
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d
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s
lim
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lear
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s
o
f
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n
o
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ly
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th
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last
v
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e
b
u
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also
o
n
h
is
to
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ical
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atter
n
s
th
at
m
ay
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o
t b
e
f
u
lly
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ep
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esen
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th
e
tr
a
in
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s
s
.
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h
e
MI
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s
tr
ateg
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p
r
o
v
id
es
r
esu
lts
f
ar
th
est
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r
o
m
t
h
e
test
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ata,
with
p
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ed
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es
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elat
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f
lat
an
d
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o
t
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ic
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v
o
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.
T
h
e
h
ig
h
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m
p
le
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ity
in
th
e
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s
tr
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au
s
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el
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im
u
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eo
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ly
,
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ak
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it
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ic
u
lt
to
ca
p
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tan
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ch
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g
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atter
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s
.
Fu
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th
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m
o
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m
et
r
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ar
e
ca
lcu
lated
u
s
in
g
R
MSE
,
MA
E
,
an
d
MA
PE.
T
h
ese
m
etr
ics
p
r
o
v
id
e
in
f
o
r
m
atio
n
a
b
o
u
t th
e
ac
cu
r
ac
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an
d
av
e
r
ag
e
er
r
o
r
o
f
th
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f
o
r
ec
asted
v
al
u
es g
en
er
ate
d
b
y
th
e
m
o
d
el.
T
h
e
p
er
f
o
r
m
a
n
ce
o
f
ea
ch
f
o
r
e
ca
s
tin
g
s
tr
ateg
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test
ed
in
T
a
b
le
3
s
h
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ws
th
at
th
e
b
est
m
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e
n
o
t
co
n
s
is
ten
tly
s
h
o
wn
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o
n
e
s
tr
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o
v
e
r
d
if
f
er
en
t
tim
e
p
er
io
d
s
.
I
n
th
e
s
h
o
r
t
ter
m
,
t
h
e
R
MSE
,
MA
E
,
an
d
MA
PE
v
alu
es
o
b
tain
e
d
f
r
o
m
all
th
r
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s
tr
ateg
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ca
n
b
e
co
n
s
id
er
ed
q
u
ite
g
o
o
d
,
with
th
e
d
ir
ec
t
s
tr
ateg
y
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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tell
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3
8
F
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r
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r
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t
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(
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2639
p
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th
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d
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est
s
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s
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atter
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m
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ig
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r
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e
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u
r
e
3
.
C
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p
a
r
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o
n
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f
test
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ata
an
d
f
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g
r
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f
o
r
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M
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Dete
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m
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T
h
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t
th
e
tr
ain
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n
g
to
ev
alu
atio
n
p
r
o
ce
s
s
,
th
e
s
tr
en
g
th
s
an
d
wea
k
n
ess
es
o
f
ea
ch
s
tr
at
eg
y
ca
n
b
e
id
en
tifie
d
.
R
ec
u
r
s
iv
e,
as
th
e
b
est
s
tr
ateg
y
f
o
r
l
o
n
g
-
te
r
m
p
r
ice
f
o
r
ec
asti
n
g
,
o
n
ly
u
s
es
a
s
i
n
g
le
-
o
u
t
p
u
t
m
o
d
el
,
th
u
s
r
eq
u
ir
in
g
less
tim
e
in
t
h
e
m
o
d
el
tr
ain
in
g
an
d
h
y
p
e
r
p
a
r
am
eter
tu
n
in
g
p
r
o
ce
s
s
.
W
ith
a
s
im
p
le
s
ch
e
m
e,
er
r
o
r
s
in
th
e
f
o
r
ec
asti
n
g
r
esu
lts
ac
cu
m
u
late
as th
e
f
o
r
ec
ast p
er
io
d
in
cr
ea
s
es.
T
h
e
wea
k
n
ess
o
f
r
ec
u
r
s
iv
e
in
ter
m
s
o
f
er
r
o
r
ac
cu
m
u
latio
n
i
s
n
o
t
ex
p
er
ien
ce
d
b
y
d
ir
ec
t
a
n
d
MI
MO
.
T
h
is
ca
n
o
cc
u
r
in
th
e
d
ir
ec
t
s
tr
ateg
y
b
ec
au
s
e
th
e
m
o
d
el
is
b
u
ilt
f
o
r
as
m
an
y
p
er
io
d
s
as
d
esi
r
ed
f
o
r
f
o
r
ec
asti
n
g
.
Ho
wev
er
,
th
e
m
ain
d
r
awb
ac
k
is
th
e
ex
ten
s
iv
e
tim
e
r
e
q
u
ir
ed
in
th
e
m
o
d
el
tr
ain
in
g
an
d
h
y
p
er
p
ar
am
eter
t
u
n
in
g
p
r
o
ce
s
s
.
Ad
d
itio
n
ally
,
th
e
d
ir
ec
t
s
tr
ateg
y
also
h
as
lim
itatio
n
s
in
ca
p
tu
r
in
g
co
m
p
le
x
tem
p
o
r
al
d
ep
e
n
d
en
cies,
esp
ec
ially
if
th
e
p
atter
n
s
an
d
r
elatio
n
s
h
ip
s
b
etwe
en
v
ar
iab
les
in
th
e
d
ata
ar
e
d
y
n
am
ic
o
r
ch
an
g
e
o
v
er
tim
e.
An
o
th
er
s
tr
ateg
y
,
MI
MO
,
o
n
l
y
u
s
es
o
n
e
m
o
d
el
th
at
m
ain
ta
in
s
tem
p
o
r
al
d
ep
en
d
en
cies
an
d
d
o
es
n
o
t
r
eq
u
ir
e
m
u
c
h
tim
e
in
th
e
tr
ain
in
g
an
d
h
y
p
er
p
a
r
am
eter
tu
n
in
g
p
r
o
ce
s
s
.
Ho
wev
er
,
MI
MO
also
h
a
s
d
is
ad
v
an
tag
es
s
u
ch
as
a
lac
k
o
f
f
le
x
ib
ilit
y
an
d
h
i
g
h
m
o
d
el
co
m
p
lex
ity
.
T
h
is
ca
u
s
es
MI
M
O
to
p
o
ten
tially
b
e
in
ef
f
ec
tiv
e
in
a
d
ap
tin
g
t
o
r
ap
i
d
an
d
c
o
m
p
lex
ch
an
g
es in
d
at
a
d
y
n
am
ics.
3
.
4
.
F
o
re
ca
s
t
ing
r
esu
lt
s
T
h
e
d
ata
u
s
ed
r
e
p
r
esen
ts
th
e
s
u
g
ar
f
u
tu
r
es
co
n
tr
ac
t p
r
ice
f
o
r
J
u
ly
2
0
2
4
,
m
ea
n
in
g
th
e
co
n
tr
a
ct
p
r
ice
is
f
o
r
ec
asted
u
n
til
th
e
last
wo
r
k
in
g
d
ay
b
e
f
o
r
e
J
u
ly
,
wh
ic
h
is
J
u
n
e
2
8
,
2
0
2
4
.
T
h
e
r
e
a
r
e
tw
o
s
tr
a
te
g
ies
,
r
e
c
u
r
s
iv
e
an
d
d
i
r
e
ct,
a
p
p
li
ed
t
o
f
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ca
s
t
s
u
g
a
r
p
r
i
ce
s
wit
h
d
i
f
f
e
r
e
n
t f
o
r
ec
as
t
ti
m
e
p
er
io
d
s
.
T
h
e
f
o
r
e
ca
s
t
r
esu
lts
i
n
F
ig
u
r
e
4
Evaluation Warning : The document was created with Spire.PDF for Python.
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2640
s
h
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s
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t
d
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s
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m
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an
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4
ac
co
r
d
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g
to
th
e
r
ec
u
r
s
iv
e
s
tr
ateg
y
.
C
o
m
p
an
ies
ca
n
u
tili
ze
th
is
in
f
o
r
m
atio
n
to
p
la
n
s
u
g
ar
p
u
r
ch
ases
d
u
r
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g
th
is
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io
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at
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ices.
T
h
is
will
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elp
th
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tim
ize
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p
en
d
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u
ce
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ctio
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c
o
s
ts
,
th
er
eb
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i
n
cr
ea
s
in
g
p
r
o
f
its
.
M
ea
n
wh
ile,
th
e
p
r
ice
f
o
r
ec
ast
s
h
o
wn
b
y
th
e
d
i
r
ec
t
s
tr
ateg
y
h
as
m
o
r
e
f
l
u
ctu
atin
g
r
esu
lts
with
p
o
ten
tial
s
h
o
r
t
-
ter
m
m
ar
k
et
v
o
latilit
y
.
T
h
e
f
o
r
ec
ast
r
esu
lts
g
en
er
ated
b
y
th
e
d
ir
ec
t
s
tr
ateg
y
ar
e
m
o
r
e
s
u
itab
le
f
o
r
tr
ad
er
s
s
ee
k
in
g
o
p
p
o
r
tu
n
ities
f
r
o
m
s
h
o
r
t
-
ter
m
p
r
ice
m
o
v
e
m
en
ts
f
o
r
s
p
ec
u
latio
n
o
r
h
e
d
g
in
g
,
tak
in
g
ad
v
a
n
tag
e
o
f
m
ar
k
et
v
o
lat
ilit
y
f
o
r
s
h
o
r
t
-
ter
m
g
ain
s
b
y
b
u
y
in
g
wh
en
p
r
ices a
r
e
lo
w
an
d
s
ellin
g
wh
en
p
r
ices r
is
e.
Fig
u
r
e
4
.
Su
g
ar
f
u
tu
r
es c
o
n
tr
a
ct
p
r
ice
f
o
r
ec
ast r
esu
lts
4.
CO
NCLU
SI
O
N
B
ased
o
n
th
e
r
esear
c
h
co
n
d
u
ct
ed
o
n
s
u
g
ar
f
u
tu
r
es
c
o
n
tr
ac
t p
r
ices,
th
e
h
y
p
e
r
p
ar
am
ete
r
tu
n
i
n
g
p
r
o
ce
s
s
h
as
v
ar
io
u
s
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ts
o
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ea
ch
m
u
lti
-
s
tep
ah
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d
f
o
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ec
asti
n
g
s
tr
ateg
y
.
T
h
e
s
tr
ateg
y
th
at
ca
n
b
e
u
s
ed
to
f
o
r
ec
ast
s
u
g
ar
p
r
ices
in
th
e
lo
n
g
ter
m
,
r
an
g
in
g
f
r
o
m
3
m
o
n
th
s
to
1
y
ea
r
,
is
r
ec
u
r
s
iv
e.
T
h
e
f
o
r
ec
a
s
ted
p
r
ices
h
av
e
a
co
n
tin
u
o
u
s
d
o
wn
wa
r
d
tr
e
n
d
,
s
o
m
ar
k
et
p
ar
ticip
an
ts
ar
e
r
e
co
m
m
en
d
e
d
to
p
lan
s
u
g
ar
p
u
r
ch
ases
to
o
p
tim
ize
co
m
p
an
y
p
r
o
f
its
.
Me
an
wh
ile,
s
h
o
r
t
-
ter
m
s
u
g
a
r
p
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ice
f
o
r
ec
asts
ar
e
b
est
d
o
n
e
b
y
a
d
ir
ec
t
s
tr
ateg
y
.
Flu
ctu
atin
g
p
r
ices
ca
n
b
e
co
n
s
id
er
e
d
b
y
tr
ad
er
s
to
tak
e
ad
v
an
ta
g
e
o
f
s
h
o
r
t
-
ter
m
tr
ad
in
g
o
p
p
o
r
tu
n
ities
t
h
at
ar
is
e
f
r
o
m
p
r
ic
e
v
o
latilit
y
,
allo
win
g
th
em
t
o
m
ak
e
q
u
ic
k
p
r
o
f
its
b
y
ca
p
italizin
g
o
n
r
ap
i
d
p
r
ice
c
h
a
n
g
es
with
in
s
h
o
r
ter
f
o
r
ec
asti
n
g
h
o
r
izo
n
s
.
Fo
r
e
ca
s
tin
g
s
u
g
ar
f
u
tu
r
es
co
n
tr
ac
t
p
r
ic
es
f
o
r
s
ev
er
al
p
e
r
io
d
s
ah
ea
d
r
em
ain
s
a
ch
allen
g
e
in
ac
h
iev
in
g
h
ig
h
ac
c
u
r
ac
y
.
T
h
er
ef
o
r
e
,
th
e
f
o
r
ec
ast
v
alu
es
an
d
p
atter
n
s
g
e
n
er
ated
ca
n
s
till
b
e
co
n
s
id
er
e
d
with
atten
tio
n
to
m
ar
k
et
co
n
d
itio
n
s
an
d
o
th
er
e
x
ter
n
al
f
ac
to
r
s
.
T
h
is
s
tu
d
y
f
o
cu
s
es
o
n
t
h
e
ap
p
licatio
n
o
f
L
STM
m
eth
o
d
u
s
in
g
u
n
iv
a
r
iate
d
ata
t
o
f
o
r
ec
ast
v
alu
es
s
ev
er
al
p
e
r
io
d
s
ah
ea
d
b
y
co
m
p
a
r
in
g
th
e
p
e
r
f
o
r
m
a
n
ce
o
f
t
h
r
ee
s
tr
ateg
ies.
Fu
tu
r
e
r
esear
ch
ca
n
ap
p
ly
o
th
er
m
o
d
elin
g
m
eth
o
d
s
th
at
ca
n
ca
p
t
u
r
e
p
atter
n
s
u
n
d
er
g
o
in
g
s
ig
n
if
ican
t
ch
an
g
es.
Ad
d
itio
n
ally
,
ad
d
in
g
o
th
er
s
tr
ateg
ies
s
u
ch
as
d
i
r
ec
t
-
r
ec
u
r
s
iv
e
(
Dir
R
ec
)
an
d
d
ir
ec
t
m
u
lti
-
o
u
t
p
u
t
(
Dir
MO
)
as
ef
f
o
r
ts
to
o
b
tain
t
h
e
m
o
s
t
ac
cu
r
ate
f
o
r
ec
asts
.
M
o
r
eo
v
e
r
,
m
u
ltiv
ar
iate
d
ata
u
s
i
n
g
e
x
ter
n
al
f
ac
to
r
s
,
s
u
ch
as
p
o
liti
ca
l
co
n
d
itio
n
s
,
g
o
v
er
n
m
e
n
t p
o
licies,
an
d
clim
a
te
ch
an
g
e
af
f
ec
tin
g
s
u
g
ar
p
r
ic
es,
ca
n
also
b
e
u
s
ed
,
s
o
th
at
th
e
f
o
r
ec
ast v
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a
ti
o
n
a
l
S
tatisti
c
a
l
In
stit
u
te
a
n
d
a
fo
rm
e
r
c
h
a
irma
n
o
f
t
h
e
In
d
o
n
e
sia
S
tatisti
c
a
l
As
so
c
iatio
n
.
H
is
re
s
e
a
rc
h
i
n
te
re
st
s
in
c
l
u
d
e
m
i
x
e
d
m
o
d
e
ls
,
sm
a
ll
a
r
e
a
e
s
ti
m
a
t
io
n
,
t
ime
se
r
ies
a
n
a
l
y
sis
,
a
n
d
sta
t
ist
ica
l
m
a
c
h
i
n
e
lea
r
n
i
n
g
.
He
c
a
n
b
e
c
o
n
tac
te
d
a
t
e
m
a
il
:
k
h
a
i
ri
l@a
p
p
s
.
i
p
b
.
a
c
.
i
d
.
K
a
y
la
Fa
k
h
r
iy
y
a
J
a
sm
in
e
h
o
ld
s
a
Ba
c
h
e
l
o
r
o
f
S
tatist
ics
d
e
g
re
e
fro
m
IP
B
Un
iv
e
rsity
,
In
d
o
n
e
sia
,
g
ra
d
u
a
ted
in
2
0
2
4
.
S
h
e
is
c
u
rre
n
tl
y
wo
r
k
in
g
a
s
a
n
in
tern
a
l
a
u
d
it
o
r
.
Du
rin
g
h
e
r
u
n
d
e
r
g
ra
d
u
a
te
st
u
d
y
,
sh
e
d
e
v
e
l
o
p
e
d
a
str
o
n
g
i
n
tere
st
in
d
a
ta
a
n
a
l
y
sis,
sta
ti
stics
,
a
n
d
m
a
c
h
in
e
lea
rn
in
g
,
p
a
rti
c
u
larl
y
in
h
o
w
d
a
ta
-
d
r
iv
e
n
m
o
d
e
ls
c
a
n
b
e
a
p
p
li
e
d
to
s
u
p
p
o
rt
d
e
c
isio
n
-
m
a
k
in
g
.
S
h
e
a
lso
g
a
in
e
d
e
x
p
e
rien
c
e
in
a
p
p
ly
i
n
g
sta
ti
stica
l
m
e
th
o
d
s
a
n
d
p
re
d
icti
v
e
tec
h
n
iq
u
e
s
to
re
a
l
-
wo
rl
d
p
r
o
b
lem
s
d
u
ri
n
g
h
e
r
c
o
u
rse
wo
r
k
a
n
d
re
se
a
rc
h
p
r
o
jec
ts.
I
n
h
e
r
c
u
rre
n
t
p
ro
fe
ss
io
n
a
l
ro
le,
sh
e
c
o
n
ti
n
u
e
s
to
e
x
p
l
o
re
h
o
w
a
n
a
l
y
ti
c
a
l
a
p
p
r
o
a
c
h
e
s
c
a
n
c
o
n
tri
b
u
te
to
p
ro
c
e
ss
imp
ro
v
e
m
e
n
t
a
n
d
p
e
rf
o
rm
a
n
c
e
e
v
a
lu
a
ti
o
n
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t:
k
a
y
lafja
s@
g
m
a
il
.
c
o
m
o
r
k
jas
m
in
e
@g
m
f
-
a
e
ro
a
sia
.
c
o
.
id
.
Dr
.
Ir
.
Ind
a
h
w
a
ti,
M.
S
i.
is
a
d
isti
n
g
u
ish
e
d
a
c
a
d
e
m
ic
a
n
d
re
se
a
rc
h
e
r
in
t
h
e
field
o
f
sta
ti
stics
.
S
h
e
e
a
rn
e
d
h
e
r
b
a
c
h
e
lo
r,
m
a
ste
r
,
a
n
d
d
o
c
t
o
ra
l
d
e
g
re
e
in
S
tatisti
c
s
fr
o
m
IP
B
Un
iv
e
rsity
,
I
n
d
o
n
e
sia
.
As
a
re
se
a
rc
h
e
r,
sh
e
h
a
s
e
x
te
n
siv
e
ly
p
u
b
l
ish
e
d
in
b
o
th
n
a
ti
o
n
a
l
a
n
d
in
tern
a
ti
o
n
a
l
jo
u
rn
a
ls.
S
h
e
h
a
s
se
rv
e
d
a
s
a
su
p
e
r
v
iso
r
o
r
m
e
m
b
e
r
o
f
th
e
su
p
e
r
v
iso
r
y
c
o
m
m
it
tee
fo
r
u
n
d
a
rg
ra
d
u
a
te,
m
a
ste
r
,
a
n
d
d
o
c
t
o
ra
l
st
u
d
e
n
ts.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
in
d
a
h
wa
ti
@a
p
p
s.i
p
b
.
a
c
.
i
d
.
Wa
n
d
e
e
Wa
n
ish
s
a
k
p
o
n
g
is
a
n
a
ss
istan
c
e
p
ro
fe
ss
o
r
a
t
De
p
a
rt
m
e
n
t
o
f
S
tatisti
c
s,
F
a
c
u
lt
y
o
f
S
c
ien
c
e
s,
Ka
se
tsa
rt
Un
iv
e
rsity
,
Th
a
il
a
n
d
.
S
h
e
c
o
m
p
l
e
ted
h
e
r
m
a
ste
r’s
d
e
g
re
e
in
A
p
p
li
e
d
S
tatisti
c
s
fr
o
m
Na
ti
o
n
a
l
In
stit
u
te
o
f
De
v
e
lo
p
m
e
n
t
Ad
m
i
n
i
stra
ti
o
n
,
Th
a
il
a
n
d
a
n
d
P
h
.
D.
in
Re
se
a
rc
h
M
e
th
o
d
o
l
o
g
y
fro
m
P
rin
c
e
o
f
S
o
n
g
k
la
Un
iv
e
rsity
,
T
h
a
il
a
n
d
.
Du
ri
n
g
t
h
e
las
t
ten
y
e
a
rs,
sh
e
h
a
s
ta
u
g
h
t
a
n
d
d
o
re
se
a
rc
h
th
e
f
o
ll
o
win
g
su
b
jec
ts:
ti
m
e
se
ries
a
n
a
ly
sis,
m
u
lt
i
v
a
riate
a
n
a
ly
sis,
re
g
re
ss
io
n
a
n
a
ly
sis
sa
m
p
li
n
g
tec
h
n
iq
u
e
,
sta
ti
stica
l
m
e
th
o
d
,
a
n
d
d
a
ta
sc
ien
c
e
.
S
h
e
c
a
n
b
e
c
o
n
tac
ted
a
t
e
m
a
il
:
wa
n
d
e
e
.
w@
k
u
.
t
h
.
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