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th
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p
a
p
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r,
a
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b
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d
m
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e
l
u
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a
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d
d
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g
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term
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m
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m
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l
b
a
se
d
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d
isc
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te
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rier
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sfo
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(DFT
)
d
e
c
o
m
p
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siti
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n
is
p
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se
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ted
.
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d
e
d
b
y
it
s
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p
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c
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m
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d
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e
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m
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ts.
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s
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lo
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t
h
e
l
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e
a
r
c
o
m
p
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n
e
n
t,
wh
il
e
DLS
TM
is ap
p
l
ied
o
n
t
h
e
n
o
n
li
n
e
a
r
c
o
m
p
o
n
e
n
t;
th
e
two
p
re
d
ictio
n
s a
re
th
e
n
c
o
m
b
in
e
d
t
o
o
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th
e
f
i
n
a
l
p
re
d
icte
d
c
o
n
su
m
p
ti
o
n
.
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e
p
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p
o
se
d
tec
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n
iq
u
e
s
a
re
a
p
p
li
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d
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h
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h
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it
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n
d
a
ta
o
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F
ra
n
c
e
to
o
b
tain
fo
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c
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sts
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r
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d
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y
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o
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e
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e
k
a
n
d
ten
d
a
y
s
a
h
e
a
d
c
o
n
su
m
p
ti
o
n
.
Th
e
re
su
l
ts
re
v
e
a
l
th
a
t
th
e
p
r
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p
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se
d
m
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tp
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s
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n
c
h
m
a
rk
m
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c
o
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sid
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d
in
th
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in
v
e
stig
a
ti
o
n
a
s
it
a
tt
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d
l
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we
r
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rro
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s.
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p
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se
d
m
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l
c
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u
ld
a
c
c
u
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tely
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p
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n
h
a
n
c
in
g
p
re
d
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n
a
c
c
u
ra
c
y
.
K
ey
w
o
r
d
s
:
ANN
AR
I
MA
DL
STM
Fo
r
ec
asti
n
g
T
im
e
s
er
ies
T
h
is i
s
a
n
o
p
e
n
a
c
c
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ss
a
rticle
u
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d
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e
CC B
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-
SA
li
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se
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C
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s
p
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A
uth
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r
:
Osma
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Yak
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b
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Dep
ar
tm
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C
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p
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ter
Scie
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Gar
d
en
C
ity
Un
iv
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s
ity
C
o
lleg
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P.O.
B
o
x
KS 1
2
7
7
5
,
Ku
m
asi,
Gh
an
a
E
m
ail:
Osma
n
.
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u
b
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@
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cu
c.
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u
.
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h
1.
I
NT
RO
D
UCT
I
O
N
Mo
d
er
n
lif
e
is
d
ep
en
d
en
t
o
n
e
lectr
icity
;
b
u
s
in
ess
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d
h
o
u
s
eh
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ld
co
n
s
u
m
e
r
s
ar
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ea
v
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r
elian
t
o
n
elec
tr
icity
f
o
r
th
eir
d
aily
en
e
r
g
y
r
e
q
u
ir
em
e
n
ts
.
Acc
u
r
ately
f
o
r
ec
asti
n
g
elec
tr
icity
co
n
s
u
m
p
tio
n
,
wh
ich
f
alls
u
n
d
er
th
e
d
o
m
ain
o
f
tim
e
s
e
r
ies
p
r
ed
ictio
n
s
,
c
o
n
tin
u
es
t
o
en
g
ag
e
th
e
atten
tio
n
o
f
r
esear
c
h
er
s
wh
o
h
av
e
em
p
lo
y
ed
v
ar
io
u
s
p
r
ed
ictio
n
tech
n
iq
u
es.
I
n
b
o
t
h
d
ev
el
o
p
e
d
an
d
d
ev
elo
p
in
g
ec
o
n
o
m
ies,
g
o
v
er
n
m
en
ts
an
d
th
eir
ag
e
n
cies
em
p
h
asize
th
e
im
p
o
r
tan
ce
o
f
p
r
e
d
ictin
g
ele
ctr
icity
co
n
s
u
m
p
tio
n
p
r
ec
is
el
y
f
o
r
p
o
licy
in
[
1
]
.
E
r
r
o
n
e
o
u
s
ly
p
r
ed
ictin
g
elec
tr
i
city
co
n
s
u
m
p
tio
n
h
as
a
n
eg
at
iv
e
f
in
a
n
cial
im
p
ac
t
[
1
]
.
Acc
u
r
ac
y
is
t
h
e
m
o
s
t
s
ig
n
if
ican
t
f
ac
to
r
c
o
n
s
id
er
ed
i
n
ch
o
o
s
in
g
a
s
u
itab
le
f
o
r
ec
asti
n
g
m
o
d
el
[
2
]
,
[
3]
.
E
lectr
icity
co
n
s
u
m
p
tio
n
d
ata
ar
e
a
tim
e
s
er
ies
s
in
ce
it
is
g
ath
er
ed
at
tim
e
i
n
ter
v
als.
I
n
f
o
r
e
ca
s
tin
g
tim
e
s
er
ies,
p
ast
o
b
s
er
v
atio
n
s
o
f
t
h
e
s
am
e
v
ar
iab
le
ar
e
g
ath
er
e
d
f
o
r
an
al
y
s
is
to
d
ev
elo
p
a
m
o
d
el
to
b
e
u
s
ed
f
o
r
p
r
ed
ictin
g
f
u
tu
r
e
v
al
u
es
[
4
]
.
Mo
s
t
r
ea
l
-
life
tim
e
s
er
ies
d
ataset
s
in
clu
d
in
g
wea
th
e
r
,
elec
tr
icity
co
n
s
u
m
p
tio
n
,
a
n
d
o
il
f
ield
p
r
o
d
u
ctio
n
h
av
e
th
e
s
eq
u
en
tial
p
r
o
p
er
ty
o
f
tim
e.
S
o
f
in
d
in
g
an
e
f
f
ec
tiv
e
tec
h
n
iq
u
e
f
o
r
tr
en
d
f
o
r
ec
asti
n
g
co
n
tin
u
es
to
b
e
a
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
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J
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Sci,
Vo
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24
,
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ch
allen
g
e
[
5
]
,
[
6
]
.
Owin
g
t
o
its
u
n
iq
u
e
p
r
o
p
e
r
ties
,
tim
e
s
er
ies
f
o
r
ec
asti
n
g
ac
cu
r
ac
y
is
o
n
e
o
f
th
e
m
o
s
t
ch
allen
g
in
g
p
r
o
b
lem
s
in
d
ata
m
in
in
g
[
7
]
.
T
im
e
s
er
ies
d
ata
ca
n
s
h
o
w
d
iv
er
s
e
c
o
m
p
o
n
e
n
ts
s
u
ch
as
tr
en
d
s
,
s
ea
s
o
n
ality
,
an
d
ju
m
p
s
[
8
]
.
Si
n
g
le
m
o
d
els
th
at
h
av
e
b
ee
n
u
s
ed
f
o
r
tim
e
-
s
er
ies
f
o
r
ec
asti
n
g
h
a
v
e
b
ee
n
f
o
u
n
d
d
ef
ici
en
t
in
f
o
r
ec
asti
n
g
ac
cu
r
a
cy
[
4
]
.
H
y
b
r
id
m
o
d
els
h
av
e
b
ee
n
id
en
tifie
d
as
th
e
b
est
in
te
r
m
s
o
f
f
o
r
ec
asti
n
g
ac
cu
r
ac
y
[
4
]
,
[
9
]
.
I
n
a
co
m
p
r
eh
en
s
iv
e
r
ev
iew
b
y
[
2
]
,
it
was
d
is
co
v
er
ed
th
at
h
y
b
r
i
d
m
e
th
o
d
s
ar
e
th
e
m
o
s
t
s
u
itab
le
an
d
ac
cu
r
ate
m
eth
o
d
s
f
o
r
f
o
r
ec
asti
n
g
tim
e
s
er
ies.
P
ar
allel
-
s
er
ies
h
y
b
r
id
s
tr
u
ctu
r
es
co
u
ld
also
p
r
o
v
id
e
m
o
r
e
p
r
ec
is
e
an
d
p
r
o
m
is
in
g
r
e
s
u
lts
co
m
p
ar
ed
to
o
n
ly
h
y
b
r
id
m
eth
o
d
s
[
2
]
.
T
im
e
s
er
ies
d
ata
s
u
ch
as
elec
tr
icity
co
n
s
u
m
p
tio
n
co
u
l
d
b
e
c
o
m
p
o
s
ed
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
c
o
m
p
o
n
e
n
ts
,
an
d
a
s
in
g
le
m
o
d
el
m
ay
n
o
t
p
r
o
v
id
e
a
n
ac
cu
r
ate
f
o
r
ec
ast
a
u
to
r
e
g
r
ess
iv
e
in
teg
r
ated
m
o
v
in
g
a
v
er
ag
e
(
AR
I
MA
)
h
as b
e
en
wid
ely
u
s
ed
in
f
o
r
ec
asti
n
g
th
e
lin
ea
r
co
m
p
o
n
e
n
ts
o
f
tim
e
s
er
ies
[
4
]
,
[
9
]
,
an
d
it
is
wid
e
ly
ac
k
n
o
wled
g
e
d
th
at
ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
m
o
d
el
th
e
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
o
f
tim
e
s
er
ies
m
o
r
e
ac
cu
r
atel
y
[
1
0
]
.
AR
I
MA
is
a
tr
ad
itio
n
al
s
tatis
t
ical
m
eth
o
d
u
s
ed
i
n
tim
e
s
er
ies
f
o
r
ec
asti
n
g
[
1
1
]
.
E
f
f
ec
t
iv
e
tech
n
iq
u
es
ca
p
ab
le
o
f
s
p
litt
in
g
th
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
in
to
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
e
n
ts
to
b
e
m
o
d
eled
d
if
f
er
e
n
tly
an
d
co
m
b
i
n
ed
f
o
r
a
n
ef
f
ec
tiv
e
f
o
r
ec
ast,
ar
e
th
er
ef
o
r
e
d
esire
d
.
Mo
tiv
ated
b
y
th
e
p
o
s
s
ib
ilit
y
o
f
m
o
d
ellin
g
lin
ea
r
an
d
n
o
n
-
lin
ea
r
co
m
p
o
n
en
ts
o
f
tim
e
s
er
ies
d
ata
s
ep
ar
ately
to
o
b
tain
m
o
r
e
a
cc
u
r
ate
p
r
e
d
ictio
n
s
,
we
p
r
o
p
o
s
e
a
h
y
b
r
i
d
a
u
to
r
eg
r
ess
iv
e
in
teg
r
ated
m
o
v
in
g
av
er
ag
e
-
d
ee
p
lo
n
g
s
h
o
r
t
ter
m
m
em
o
r
y
(
AR
I
MA
-
DL
STM
)
m
o
d
el
b
ased
o
n
d
is
cr
ete
f
o
u
r
i
er
tr
an
s
f
o
r
m
(
DFT)
to
f
o
r
ec
ast
d
aily
elec
tr
icity
c
o
n
s
u
m
p
tio
n
.
T
h
e
p
r
o
p
o
s
ed
AR
I
MA
-
DL
STM
m
o
d
el
is
em
p
l
o
y
ed
t
o
o
b
tain
o
n
e
-
s
tep
-
ah
ea
d
,
o
n
e
-
week
-
ah
ea
d
,
an
d
1
0
-
d
ay
s
-
ah
ea
d
p
r
ed
ictio
n
s
.
Usi
n
g
ro
o
t
m
ea
n
s
q
u
ar
e
er
r
o
r
(
R
MSE
)
,
m
ea
n
ab
s
o
lu
te
p
er
ce
n
ta
g
e
er
r
o
r
(
M
APE)
,
an
d
m
ea
n
ab
s
o
lu
te
er
r
o
r
(
MA
E
)
,
t
h
e
p
r
o
p
o
s
ed
m
o
d
el
is
co
m
p
ar
ed
with
s
ix
r
ef
er
en
ce
m
o
d
els.
T
h
e
p
r
o
p
o
s
ed
AR
I
MA
-
DL
STM
m
o
d
el
ac
h
iev
e
d
a
lo
wer
er
r
o
r
m
ea
s
u
r
e
th
a
n
th
e
r
ef
er
en
ce
m
o
d
els,
i
n
f
er
r
i
n
g
t
h
at
it
o
u
t
p
er
f
o
r
m
s
th
e
r
ef
er
e
n
ce
d
m
o
d
els
in
p
r
ed
ictio
n
ac
cu
r
ac
y
b
ec
au
s
e
th
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
wer
e
d
ec
o
m
p
o
s
ed
m
o
r
e
ac
cu
r
ately
.
T
h
e
r
est
o
f
t
h
e
p
a
p
er
is
o
r
g
a
n
ized
as
f
o
llo
ws,
in
s
ec
tio
n
2
,
r
elate
d
wo
r
k
is
d
is
cu
s
s
ed
,
a
n
d
s
ec
tio
n
3
co
n
tain
s
th
e
p
r
o
p
o
s
ed
AR
I
MA
-
DL
STM
m
o
d
el.
Sectio
n
4
d
escr
ib
es
th
e
d
etails
o
f
th
e
ex
p
er
im
en
tal
s
etu
p
f
o
llo
wed
b
y
th
e
ex
p
er
im
en
tal
r
esu
lts
wh
ich
ar
e
p
r
esen
ted
an
d
d
is
cu
s
s
ed
in
s
ec
tio
n
5
.
T
h
e
p
ap
er
is
co
n
clu
d
ed
in
s
ec
tio
n
6
.
2.
RE
L
AT
E
D
WO
RK
A
n
u
m
b
er
o
f
ap
p
r
o
ac
h
es
h
av
e
b
ee
n
p
r
esen
ted
to
o
v
er
c
o
m
e
th
e
ch
allen
g
es
ass
o
ciate
d
with
tim
e
-
s
er
ies
f
o
r
ec
asti
n
g
,
in
g
en
er
a
l,
an
d
elec
tr
icity
co
n
s
u
m
p
ti
o
n
tim
e
s
er
ies
f
o
r
ec
asti
n
g
in
p
ar
ticu
lar
.
T
h
ese
p
r
o
p
o
s
ed
m
eth
o
d
s
ca
n
b
e
clas
s
if
ied
as
s
tatis
tical
an
d
s
o
f
t
c
o
m
p
u
tin
g
tech
n
i
q
u
es.
AR
I
MA
an
d
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANN
)
m
o
d
els
ar
e
ex
p
lo
r
ed
b
y
[
9
]
a
n
d
a
n
o
v
el
h
y
b
r
id
AR
I
MA
-
ANN
m
o
d
el
is
d
ev
is
ed
f
o
r
th
e
f
o
r
ec
asti
n
g
o
f
tim
e
s
er
ies
d
ata
.
T
h
e
v
o
latile
n
atu
r
e
o
f
tim
e
s
er
ies
is
ex
p
lo
r
e
d
b
y
d
ec
o
m
p
o
s
in
g
th
e
tim
e
s
er
ies
d
ata
in
to
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
e
n
ts
u
s
in
g
an
MA
f
ilter
th
at
ac
h
iev
ed
b
etter
p
r
e
d
ictio
n
ac
cu
r
ac
y
th
a
n
in
d
iv
id
u
al
AR
I
MA
an
d
ANN
m
o
d
els
an
d
t
h
e
h
y
b
r
id
AR
I
MA
-
ANN
m
o
d
el
p
r
esen
ted
in
[
4
]
.
I
n
[
1
0
]
,
a
n
ANN
m
o
d
el
b
ased
o
n
an
m
u
ltil
ay
er
p
er
ce
p
tr
o
n
(
MLP
)
with
a
b
ac
k
p
r
o
p
a
g
atio
n
tr
ain
in
g
alg
o
r
ith
m
,
wh
ich
is
u
s
ed
as
th
e
n
eu
tr
al
n
etwo
r
k
to
p
o
lo
g
y
was
p
r
o
p
o
s
ed
to
p
r
ed
ict
t
h
e
elec
tr
icity
co
n
s
u
m
p
tio
n
o
f
T
u
r
k
e
y
.
T
a
n
g
en
t
-
s
ig
m
o
id
an
d
p
u
r
e
-
lin
ea
r
tr
an
s
f
er
f
u
n
ctio
n
s
wer
e
s
elec
ted
i
n
th
e
h
id
d
en
a
n
d
o
u
ter
la
y
er
p
r
o
ce
s
s
in
g
elem
en
ts
,
r
esp
ec
tiv
el
y
.
A
n
o
v
el
d
ee
p
l
ea
r
n
in
g
f
o
r
ec
asti
n
g
m
o
d
el
th
at
ex
p
lo
its
th
e
ab
ilit
y
o
f
co
n
v
o
lu
tio
n
al
lay
e
r
s
to
ex
tr
ac
t
u
s
ef
u
l
k
n
o
wled
g
e
a
n
d
th
e
ef
f
icac
y
o
f
lo
n
g
s
h
o
r
t
-
ter
m
m
em
o
r
y
(
L
STM
)
lay
er
s
f
o
r
th
e
id
en
tific
atio
n
o
f
s
h
o
r
t
-
ter
m
an
d
l
o
n
g
-
ter
m
d
ep
en
d
en
cies
f
o
r
ac
c
u
r
ate
f
o
r
ec
a
s
tin
g
o
f
g
o
ld
p
r
ices
was
p
r
esen
ted
b
y
[
1
2
]
.
T
h
ey
co
n
ten
d
th
at
t
h
e
u
s
e
o
f
L
STM
lay
er
s
to
g
et
h
er
with
ad
d
itio
n
al
co
n
v
o
lu
tio
n
al
lay
er
s
co
u
ld
en
h
an
ce
f
o
r
ec
asti
n
g
p
er
f
o
r
m
an
ce
.
I
n
f
in
an
cial
tim
e
s
er
ies,
ac
cu
r
ately
f
o
r
ec
asti
n
g
s
to
ck
p
r
ices
is
a
ch
allen
g
in
g
task
b
ec
au
s
e
th
er
e
ar
e
d
r
awb
ac
k
s
,
s
u
ch
as
th
e
u
n
s
u
itab
ilit
y
o
f
s
o
m
e
m
o
d
els
th
a
t
d
o
n
o
t
f
o
llo
w
s
tatis
tical
ass
u
m
p
tio
n
s
an
d
s
to
ck
d
ata
th
at
ar
e
v
er
y
n
o
is
y
.
I
n
[
1
3
]
,
a
h
y
b
r
id
tim
e
s
er
ies
ad
a
p
tiv
e
n
etwo
r
k
b
ased
o
n
a
f
u
z
zy
in
f
er
e
n
ce
s
y
s
tem
(
ANFI
S)
th
at
u
s
es
em
p
ir
ical
m
o
d
e
d
ec
o
m
p
o
s
itio
n
was
p
r
o
p
o
s
ed
to
ad
d
r
ess
th
ese
d
r
awb
ac
k
s
.
T
im
e
s
er
ies
co
u
ld
b
e
p
u
r
ely
lin
ea
r
,
p
u
r
ely
n
o
n
lin
ea
r
,
o
r
h
y
b
r
i
d
an
d
an
y
p
r
o
p
o
s
ed
m
o
d
el
s
h
o
u
l
d
b
e
ab
l
e
to
r
ec
o
g
n
ize
t
h
is
p
a
t
t
e
r
n
f
o
r
b
e
t
t
e
r
p
r
e
d
i
c
t
i
o
n
.
I
n
[
1
4
]
,
a
n
e
w
h
y
b
r
i
d
a
p
p
r
o
a
c
h
u
s
i
n
g
a
c
o
m
b
i
n
a
t
i
o
n
o
f
l
i
n
e
a
r
a
n
d
n
o
n
l
i
n
e
a
r
e
x
p
o
n
e
n
t
i
a
l
s
m
o
o
t
h
i
n
g
m
o
d
e
l
s
f
r
o
m
t
h
e
i
n
n
o
v
a
t
i
o
n
s
t
a
t
e
s
p
a
c
e
(
E
T
S
)
w
i
t
h
a
r
t
i
f
i
c
i
a
l
n
e
u
r
a
l
n
e
t
w
o
r
k
s
(
E
T
S
-
A
N
N
)
th
at
en
h
an
ce
th
e
p
o
s
s
ib
ilit
y
o
f
p
ick
in
g
u
p
th
e
v
ar
ied
c
o
m
b
in
atio
n
s
o
f
lin
ea
r
an
d
/o
r
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
in
h
er
en
t in
tim
e
s
er
ies wa
s
p
r
o
p
o
s
ed
.
T
o
p
r
ed
ict
s
h
o
r
t
-
te
r
m
r
esid
e
n
tial
el
ec
tr
icity
co
n
s
u
m
p
tio
n
in
C
h
in
a,
a
h
y
b
r
id
h
o
lt
–
wi
n
ter
s
(
HW
)
m
eth
o
d
an
d
an
ex
tr
em
e
lear
n
in
g
m
ac
h
in
e
(
E
L
M)
n
etwo
r
k
was
p
r
o
p
o
s
ed
b
y
[
1
5
]
.
T
h
e
o
r
ig
in
al
d
ata
ar
e
d
ec
o
m
p
o
s
ed
in
to
lin
ea
r
a
n
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
u
s
in
g
a
m
o
v
in
g
a
v
er
ag
e
f
ilter
.
T
h
e
H
W
m
eth
o
d
is
u
s
ed
to
m
o
d
el
th
e
lin
ea
r
co
m
p
o
n
en
t,
wh
ile
E
L
M
is
u
s
ed
to
f
o
r
ec
ast th
e
n
o
n
lin
ea
r
m
o
d
el,
a
n
d
th
e
r
esu
lts
ar
e
co
m
b
in
ed
to
p
r
ed
ict
1
5
-
m
in
u
te
elec
tr
icit
y
co
n
s
u
m
p
tio
n
.
Fu
r
th
er
,
p
ar
titi
o
n
in
g
an
d
in
ter
p
o
latio
n
(
PI)
b
ased
AR
I
MA
-
ANN
m
o
d
el
[
1
6
]
o
u
tp
er
f
o
r
m
e
d
MA
f
ilter
b
as
ed
AR
I
MA
-
ANN
tech
n
iq
u
e
i
n
f
o
r
ec
asti
n
g
tim
e
s
er
ies
d
ata.
I
n
[
1
7
]
,
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
lectricity c
o
n
s
u
mp
tio
n
fo
r
ec
a
s
tin
g
u
s
in
g
DF
T d
ec
o
m
p
o
s
itio
n
b
a
s
ed
h
yb
r
id
…
(
Osma
n
Ya
ku
b
u
)
1109
a
n
o
v
el
tim
e
s
er
ies
p
r
ed
ictio
n
m
o
d
el
ter
m
ed
Ser
iesNet,
ca
p
ab
le
o
f
co
m
p
letely
lear
n
in
g
tim
e
s
er
ies
d
at
a
f
ea
tu
r
es
at
d
if
f
e
r
en
t
in
te
r
v
als
was
p
r
esen
ted
.
T
h
e
m
o
d
el
is
ca
p
ab
le
o
f
lear
n
in
g
m
u
lti
-
r
an
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d
m
u
lti
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es
f
r
o
m
tim
e
s
er
ies
an
d
i
m
p
r
o
v
es
g
e
n
er
aliza
tio
n
b
y
ad
o
p
tin
g
r
esid
u
al
lear
n
in
g
an
d
b
atch
n
o
r
m
aliza
tio
n
,
r
esu
ltin
g
in
a
h
ig
h
e
r
p
r
ed
ictiv
e
ab
ilit
y
.
I
n
[
1
8
]
,
a
tech
n
i
q
u
e
b
ased
o
n
d
ee
p
lear
n
in
g
to
d
ea
l
with
th
e
ch
allen
g
es
o
f
f
o
r
ec
asti
n
g
b
ig
d
ata
tim
e
s
er
ies
was
also
p
r
o
p
o
s
ed
.
T
h
e
d
ee
p
f
o
r
war
d
n
e
u
r
al
n
etwo
r
k
o
f
th
e
H2
0
b
i
g
d
ata
an
aly
s
is
f
r
am
ewo
r
k
is
u
s
ed
wh
er
e
th
e
p
r
o
b
lem
at
h
an
d
i
s
s
p
lit
in
to
f
o
r
ec
asti
n
g
s
u
b
-
p
r
o
b
lem
s
.
A
h
y
b
r
id
s
y
s
tem
th
at
lo
o
k
s
f
o
r
an
ap
p
r
o
p
r
iate
f
u
n
ctio
n
to
c
o
m
b
in
e
li
n
ea
r
an
d
n
o
n
lin
ea
r
m
o
d
el
f
o
r
ec
asts
wa
s
p
r
esen
ted
by
[
1
9
]
.
An
AR
I
MA
m
o
d
el
is
u
s
ed
o
n
th
e
lin
ea
r
c
o
m
p
o
n
en
t
,
an
d
ML
P
a
n
d
s
u
p
p
o
r
t
v
ec
to
r
r
eg
r
ess
io
n
m
o
d
el,
two
in
tellig
en
t n
o
n
lin
ea
r
m
o
d
els,
ar
e
u
s
ed
o
n
t
h
e
n
o
n
lin
ea
r
co
m
p
o
n
en
t.
ANNs
h
av
e
b
ee
n
u
s
ed
wid
el
y
in
e
n
e
r
g
y
p
r
ed
ictio
n
f
o
r
a
lo
n
g
tim
e.
T
o
im
p
r
o
v
e
th
e
p
r
ed
ictio
n
ac
cu
r
ac
y
f
o
r
elec
tr
icity
co
n
s
u
m
p
tio
n
in
t
h
e
s
h
o
r
t
ter
m
,
a
ty
p
e
o
f
o
p
tim
ized
ANN
m
o
d
el
f
o
r
p
r
ed
ictin
g
h
o
u
r
ly
b
u
ild
in
g
elec
tr
icity
c
o
n
s
u
m
p
t
io
n
was
p
r
esen
ted
in
[
1
9
]
.
A
d
ee
p
lear
n
in
g
-
b
ased
f
r
am
e
wo
r
k
f
o
r
elec
tr
icity
d
em
an
d
f
o
r
ec
asti
n
g
th
at
co
n
s
id
er
s
lo
n
g
-
ter
m
h
is
to
r
ical
d
ep
en
d
en
cies
was
also
p
r
esen
ted
in
[
2
0
]
.
C
lu
s
ter
an
aly
s
is
is
in
itially
ex
ec
u
ted
o
n
th
e
elec
tr
icity
c
o
n
s
u
m
p
tio
n
d
ata
f
o
r
all
m
o
n
t
h
s
,
an
d
s
ea
s
o
n
-
b
ased
s
eg
m
e
n
ted
d
ata
ar
e
g
e
n
er
ated
.
L
o
ad
t
r
e
n
d
ch
ar
ac
ter
izatio
n
is
p
e
r
f
o
r
m
ed
to
o
b
tain
a
d
ee
p
e
r
u
n
d
er
s
tan
d
in
g
o
f
m
etad
ata
b
y
ev
alu
atin
g
ea
c
h
o
f
th
e
clu
s
te
r
s
.
Fu
r
th
er
,
t
h
ey
tr
ai
n
ed
L
ST
M
m
u
lti
-
in
p
u
t
an
d
o
u
tp
u
t
m
o
d
els
to
p
r
e
d
ict
th
e
d
em
an
d
f
o
r
elec
tr
icity
d
e
p
en
d
in
g
o
n
th
e
s
ea
s
o
n
,
d
a
y
,
an
d
in
ter
v
al.
T
o
im
p
r
o
v
e
th
e
p
r
e
d
ictio
n
r
esu
lts
,
th
ey
in
co
r
p
o
r
ated
th
e
co
n
ce
p
t
o
f
m
o
v
in
g
-
win
d
o
w
-
b
ased
ac
tiv
e
le
ar
n
in
g
.
An
L
STM
-
b
ased
s
h
o
r
t
-
ter
m
tim
e
-
p
h
ased
elec
tr
icity
co
n
s
u
m
p
tio
n
p
r
ed
ictio
n
m
o
d
el
with
a
n
atten
tio
n
m
ec
h
a
n
is
m
was
also
p
r
o
p
o
s
ed
b
y
[
2
1
]
.
T
h
e
tech
n
iq
u
e
ass
ig
n
s
a
weig
h
t
co
ef
f
icien
t
to
th
e
in
p
u
t
s
eq
u
en
ce
d
ata.
T
h
e
n
,
th
e
o
u
tp
u
t
d
ata
o
f
ea
ch
ce
ll
o
f
th
e
L
STM
ar
e
co
m
p
u
ted
u
s
in
g
th
e
f
o
r
war
d
p
r
o
p
a
g
atio
n
tec
h
n
iq
u
e.
T
h
e
b
ac
k
p
r
o
p
a
g
atio
n
tech
n
iq
u
e
was
u
s
ed
to
ca
lcu
late
th
e
er
r
o
r
b
etwe
en
th
e
r
ea
l
an
d
p
r
ed
icted
v
alu
es.
T
o
f
o
r
ec
ast
elec
tr
icity
co
n
s
u
m
p
tio
n
ac
cu
r
ately
,
a
tech
n
iq
u
e
o
f
p
r
o
b
ab
ilit
y
d
en
s
ity
f
o
r
ec
asti
n
g
b
ased
o
n
t
h
e
le
ast
ab
s
o
lu
te
s
h
r
in
k
ag
e
an
d
s
elec
tio
n
o
p
er
at
o
r
an
d
th
e
q
u
an
tile r
eg
r
ess
io
n
n
e
u
r
al
n
etwo
r
k
(
L
ASSO
-
QR
NN)
wa
s
p
r
esen
ted
in
[
2
2
]
.
T
o
f
o
r
ec
as
t
p
r
ec
is
ely
th
e
to
tal
an
d
in
d
u
s
tr
ial
elec
tr
icity
co
n
s
u
m
p
tio
n
o
f
C
h
in
a,
a
m
o
d
if
ied
g
r
ay
p
r
ed
ictio
n
m
o
d
el
t
h
at
co
m
b
in
es
a
n
ew
in
itial
co
n
d
itio
n
an
d
a
r
o
llin
g
m
ec
h
an
is
m
was
p
r
o
p
o
s
ed
in
[
2
3
]
.
T
h
ey
em
p
lo
y
ed
a
p
ar
ticle
s
war
m
o
p
tim
izatio
n
alg
o
r
ith
m
to
g
en
er
ate
p
ar
am
et
er
s
th
at
ca
n
b
e
d
eter
m
i
n
ed
o
p
t
im
ally
in
ac
co
r
d
a
n
ce
with
v
ar
i
o
u
s
f
ea
tu
r
es
o
f
t
h
e
in
p
u
t
d
ata.
A
n
in
te
g
r
ated
a
p
p
r
o
ac
h
f
o
r
t
h
e
2
4
h
o
u
r
-
a
h
ea
d
p
r
ed
ictio
n
o
f
elec
tr
icity
c
o
n
s
u
m
p
tio
n
in
b
u
ild
i
n
g
s
u
s
in
g
th
e
h
ilb
er
t
–
h
u
a
n
g
t
r
an
s
f
o
r
m
(
HHT
)
,
r
eg
r
o
u
p
in
g
p
ar
tic
le
s
war
m
o
p
tim
iz
ati
o
n
,
a
n
d
ANFI
S
was
p
r
o
p
o
s
ed
b
y
[
2
4
]
.
T
h
e
r
e
ar
e
co
m
p
lex
iti
es
an
d
u
n
ce
r
tain
ties
in
th
e
el
ec
tr
icity
s
y
s
tem
.
A
s
elf
-
ad
a
p
tiv
e
g
r
a
y
f
r
ac
tio
n
al
weig
h
ted
m
o
d
el
f
o
r
th
e
ac
c
u
r
ate
p
r
ed
ictio
n
o
f
th
e
city
o
f
J
ian
g
s
u
’
s
elec
tr
icity
co
n
s
u
m
p
tio
n
was
also
p
r
esen
ted
b
y
[
2
5
]
.
T
h
e
s
h
o
r
t
-
f
alls
o
f
AR
I
MA
in
ac
cu
r
ately
p
r
ed
ictin
g
tim
e
s
er
ies
d
ata
th
at
h
av
e
a
b
len
d
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
c
o
m
p
o
n
en
ts
co
m
p
el
led
f
ac
eb
o
o
k
to
in
tr
o
d
u
ce
p
r
o
p
h
et
,
wh
ich
is
an
o
p
e
n
-
s
o
u
r
c
e
p
r
ed
ictio
n
m
o
d
el
b
ased
o
n
d
ec
o
m
p
o
s
ab
le
m
o
d
e
ls
f
o
r
d
ata
with
tr
en
d
s
,
s
e
aso
n
ality
,
an
d
h
o
lid
ay
s
.
I
t
is
r
ep
u
t
ed
to
f
o
r
ec
ast
tim
e
s
er
ies
m
o
r
e
ac
cu
r
ately
b
y
em
p
lo
y
in
g
s
im
p
le,
in
tu
itiv
e
p
ar
a
m
eter
s
an
d
ca
n
in
clu
d
e
cu
s
to
m
s
ea
s
o
n
ality
an
d
h
o
lid
ay
s
[
2
6
]
.
T
h
e
u
s
e
o
f
an
im
p
r
o
v
e
d
p
a
r
ticle
s
war
m
o
p
ti
m
izatio
n
in
d
esig
n
in
g
a
h
y
b
r
i
d
p
r
e
d
icti
o
n
m
o
d
el
f
o
r
f
u
tu
r
e
p
r
ed
ictio
n
o
f
elec
tr
icity
co
n
s
u
m
p
tio
n
ca
n
s
ig
n
if
ican
tly
im
p
r
o
v
e
p
r
e
d
ictio
n
ac
cu
r
ac
y
[
2
7
]
.
Acc
o
r
d
in
g
to
[
2
8
]
,
f
o
r
ec
asti
n
g
elec
tr
icity
c
o
n
s
u
m
p
tio
n
i
n
h
o
u
s
eh
o
ld
s
is
c
h
allen
g
in
g
,
th
e
y
th
u
s
d
ev
elo
p
e
d
a
n
en
h
an
ce
d
s
u
p
p
o
r
t
v
ec
to
r
r
e
g
r
ess
io
n
m
o
d
el
with
th
e
c
ap
ab
ilit
y
o
f
f
o
r
ec
asti
n
g
h
o
u
s
eh
o
ld
elec
tr
icity
co
n
s
u
m
p
tio
n
th
r
o
u
g
h
s
ev
er
al
in
ter
v
en
tio
n
ap
p
r
o
ac
h
es.
A
s
u
p
p
o
r
t
v
ec
t
o
r
m
ac
h
in
e
(
SVM)
m
o
d
el
was
also
cr
ea
ted
in
[
2
9
]
to
ac
c
u
r
ately
f
o
r
ec
ast
en
er
g
y
c
o
n
s
u
m
p
tio
n
i
n
h
o
tel
b
u
ild
in
g
s
.
T
h
e
ca
p
ab
il
ity
an
d
p
r
ec
is
io
n
o
f
s
u
p
er
v
is
ed
m
ac
h
i
n
e
lear
n
in
g
tech
n
iq
u
es
was
ass
ess
ed
in
[
3
0
]
a
n
d
G
au
s
s
ian
p
r
o
ce
s
s
r
eg
r
ess
io
n
(
GPR
)
was
f
o
u
n
d
to
o
f
f
er
b
etter
p
r
ed
ict
io
n
s
o
f
e
n
er
g
y
co
n
s
u
m
p
tio
n
o
f
o
f
f
ice
b
u
ild
in
g
s
.
O
n
e
o
f
th
e
m
o
s
t
ef
f
ec
tiv
e
m
eth
o
d
s
em
p
lo
y
e
d
in
th
e
class
if
icatio
n
o
f
tim
e
s
er
ies
d
ata
i
s
r
ec
u
r
r
e
n
t
n
e
u
r
al
n
etwo
r
k
(
R
NN)
[
3
1
]
,
a
n
d
h
as
b
ee
n
u
s
ed
in
f
o
r
ec
asti
n
g
s
to
ck
p
r
ices
[
3
2
]
.
ANNs
h
av
e
also
b
ee
n
u
s
ed
in
th
e
im
p
r
o
v
em
en
t
o
f
f
o
r
ec
asti
n
g
f
o
r
th
e
p
r
ices
o
f
g
o
ld
[
3
3
]
.
C
o
n
v
o
lu
tio
n
al
n
e
u
r
al
n
etwo
r
k
s
h
as
b
ee
n
p
r
o
v
en
t
o
o
f
f
er
s
lig
h
tly
b
etter
p
r
ed
ictio
n
ac
cu
r
ac
y
co
m
p
a
r
ed
to
L
STM
[
3
4
]
.
T
im
e
s
er
ies
d
ata
r
elat
ed
to
esp
ec
ial
f
in
a
n
ce
c
o
u
ld
ex
h
ib
it
f
ea
t
u
r
es
o
f
v
o
latilit
y
,
it
co
u
ld
also
in
ad
d
itio
n
,
b
e
n
o
n
-
lin
ea
r
a
n
d
n
o
n
-
s
tatio
n
ar
y
,
as
it
is
s
u
s
ce
p
tib
le
to
ec
o
n
o
m
ic
f
ac
to
r
s
th
at
ar
e
ex
ter
n
al
[
3
5
]
.
No
twith
s
tan
d
in
g
th
e
n
u
m
er
o
u
s
m
o
d
els
p
r
o
p
o
s
ed
to
ac
cu
r
ately
p
r
ed
ict
elec
tr
icity
co
n
s
u
m
p
tio
n
,
en
h
a
n
ce
m
en
t
o
f
th
e
p
r
ed
ictio
n
p
er
f
o
r
m
an
ce
o
f
elec
tr
icity
co
n
s
u
m
p
tio
n
m
o
d
els
is
s
till
r
eq
u
ir
ed
.
Sev
er
al
p
r
esen
ted
m
o
d
els
ar
e
s
in
g
le
m
o
d
els
th
at
ar
e
eith
er
s
tatis
tical,
s
u
ch
as
A
R
I
MA
,
o
r
s
o
f
t
co
m
p
u
tin
g
,
s
u
ch
as
ANN,
wh
ich
in
th
e
e
s
tim
atio
n
o
f
[
4
]
d
o
n
o
t
g
e
n
er
ate
ac
cu
r
ate
p
r
e
d
ictio
n
s
wh
en
u
s
ed
in
d
iv
id
u
ally
.
T
h
e
h
y
b
r
id
m
o
d
els
p
r
esen
ted
also
r
eq
u
ir
e
g
r
ea
ter
ac
c
u
r
ac
y
,
as
th
e
tech
n
iq
u
es
em
p
lo
y
e
d
d
eg
r
ad
e
p
er
f
o
r
m
an
ce
wh
en
d
ec
o
m
p
o
s
in
g
t
h
e
d
ata
i
n
to
lin
ea
r
a
n
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
in
all
th
e
p
er
u
s
ed
liter
atu
r
e.
T
h
e
r
ef
o
r
e,
m
o
r
e
en
h
an
ce
d
tech
n
iq
u
es
s
h
o
u
ld
b
e
d
is
co
v
er
ed
t
h
at
ac
c
u
r
ately
d
ec
o
m
p
o
s
e
elec
tr
icity
co
n
s
u
m
p
tio
n
tim
e
s
er
ies
d
ata
in
to
its
lin
ea
r
an
d
n
o
n
lin
ea
r
c
o
m
p
o
n
en
ts
,
an
d
r
o
b
u
s
t
s
tatis
t
ical
an
d
s
o
f
t
co
m
p
u
tin
g
m
o
d
els
co
u
ld
b
e
h
y
b
r
id
ized
f
o
r
m
o
r
e
r
eliab
l
e
p
r
ed
ictio
n
s
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
2
,
No
v
em
b
er
2
0
2
1
:
1
1
0
7
-
1
1
2
0
1110
I
n
s
u
m
m
ar
y
,
a
s
ig
n
if
ica
n
t
n
u
m
b
er
o
f
r
esear
ch
o
n
e
n
h
an
cin
g
tim
e
s
er
ies
p
r
ed
ictio
n
ac
c
u
r
a
cy
h
as
b
ee
n
ex
p
lo
r
ed
.
All
th
e
r
esear
ch
e
x
p
lo
r
ed
h
a
v
e
co
n
f
ir
m
ed
t
h
at
s
in
g
le
m
o
d
els
lack
th
e
ca
p
ab
ilit
y
t
o
p
r
o
d
u
ce
ac
c
u
r
ate
f
o
r
ec
ast
s
in
ce
th
ey
ass
u
m
e
th
at
th
e
d
ata
ar
e
p
u
r
ely
lin
ea
r
o
r
p
u
r
ely
n
o
n
lin
ea
r
a
n
d
h
y
b
r
id
m
o
d
el
s
ar
e
r
eq
u
ir
e
d
.
Hy
b
r
id
m
o
d
els
r
eq
u
ir
e
th
e
d
ec
o
m
p
o
s
itio
n
o
f
th
e
d
at
a
in
to
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
.
T
h
e
d
ec
o
m
p
o
s
itio
n
tech
n
i
q
u
es
co
n
tin
u
e
to
p
r
esen
t
ch
allen
g
es
as
q
u
ality
o
f
p
r
ed
ictio
n
s
ar
e
d
eg
r
ad
ed
d
u
e
to
in
ef
f
ec
tiv
e
d
e
co
m
p
o
s
itio
n
tec
h
n
iq
u
es.
T
o
e
n
s
u
r
e
a
m
o
r
e
ac
c
u
r
ate
f
o
r
ec
ast o
f
elec
tr
icity
co
n
s
u
m
p
tio
n
,
s
u
p
er
io
r
d
ec
o
m
p
o
s
itio
n
tech
n
iq
u
es th
at
d
o
n
o
t d
eg
r
ad
e
th
e
q
u
ality
o
f
p
r
ed
ictio
n
s
ar
e
th
u
s
d
esire
d
.
3.
P
RO
P
O
SE
D
M
O
D
E
L
In
th
is
p
a
p
er
,
a
n
ew
h
y
b
r
id
AR
I
MA
-
DL
STM
p
r
ed
ictio
n
m
o
d
el
b
ased
o
n
DFT
d
ec
o
m
p
o
s
itio
n
is
p
r
esen
ted
.
E
lectr
icity
co
n
s
u
m
p
tio
n
tim
e
s
er
ies
h
av
e
tr
en
d
s
an
d
s
ea
s
o
n
ality
;
co
n
s
u
m
p
tio
n
f
o
r
in
d
u
s
tr
y
is
v
er
y
h
ig
h
d
u
r
i
n
g
p
ar
ticu
lar
tim
es
a
n
d
d
ay
s
,
s
u
c
h
as p
ea
k
wo
r
k
in
g
h
o
u
r
s
,
a
n
d
v
er
y
lo
w
at
o
th
er
t
im
es,
s
u
ch
as
b
r
ea
k
tim
es
an
d
h
o
lid
ay
s
.
T
h
e
co
n
s
u
m
p
tio
n
o
f
d
o
m
esti
c
u
s
er
s
is
h
ig
h
er
o
n
wee
k
en
d
s
an
d
h
o
lid
ay
s
wh
en
th
ey
a
r
e
h
o
m
e,
wh
ile
th
eir
co
n
s
u
m
p
tio
n
is
lo
w
wh
e
n
th
e
y
a
r
e
at
w
o
r
k
.
T
h
is
im
p
lies
th
at
elec
tr
icity
co
n
s
u
m
p
tio
n
d
at
a
ar
e
co
m
p
o
s
ed
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
e
n
ts
.
I
n
d
u
s
tr
ial
an
d
d
o
m
esti
c
elec
tr
icity
h
av
e
th
e
s
am
e
ch
ar
ac
ter
is
tics
.
T
ec
h
n
iq
u
es
m
u
s
t
b
e
em
p
lo
y
ed
to
s
eg
r
eg
ate
p
r
ec
is
ely
th
e
lin
ea
r
an
d
n
o
n
li
n
ea
r
co
m
p
o
n
en
ts
o
f
th
e
d
ata
to
m
o
d
el
th
em
f
o
r
p
r
ed
ictio
n
.
I
n
t
h
e
h
y
b
r
id
m
o
d
els
p
r
esen
ted
b
y
[
4
]
an
d
[
3
6
]
,
th
e
ass
u
m
p
tio
n
is
th
at
th
e
d
ata
ar
e
a
s
u
m
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
.
Ho
wev
er
,
th
e
d
ata
ar
e
n
o
t
d
ec
o
m
p
o
s
ed
i
n
to
co
m
p
o
n
en
ts
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
;
in
s
tead
,
an
AR
I
MA
m
o
d
el
is
ap
p
lied
d
ir
ec
tly
to
th
e
d
ata,
an
d
th
e
r
esid
u
al
er
r
o
r
is
m
o
d
eled
as
a
n
o
n
li
n
ea
r
c
o
m
p
o
n
en
t,
wh
ich
d
eg
r
a
d
es
p
er
f
o
r
m
a
n
ce
.
T
h
e
m
eth
o
d
o
l
o
g
y
o
f
th
e
p
r
o
p
o
s
ed
AR
I
MA
-
DL
STM
elec
tr
icity
co
n
s
u
m
p
tio
n
p
r
ed
icti
o
n
m
o
d
el
is
s
h
o
wn
in
Fig
u
r
e
1
(
a)
,
Fig
u
r
e
1
(
b
)
also
s
h
o
ws th
e
ar
ch
itectu
r
e
o
f
th
e
DL
STM
r
ec
u
r
r
en
t
n
etwo
r
k
.
(
a)
(
b
)
Fig
u
r
e
1
.
T
h
ese
f
ig
u
r
es a
r
e;
(
a
)
Pro
p
o
s
ed
p
r
ed
ictio
n
m
eth
o
d
,
(
b
)
DL
STM
r
ec
u
r
r
en
t
n
etwo
r
k
ar
ch
itectu
r
e
Usi
n
g
DFT,
th
e
elec
tr
icity
co
n
s
u
m
p
tio
n
tim
e
s
er
ies
is
co
n
v
er
ted
in
to
Fo
u
r
ier
co
e
f
f
icien
ts
.
First,
a
lo
w
-
p
ass
f
ilter
is
u
s
ed
to
is
o
late
Fo
u
r
ier
co
ef
f
icien
ts
th
at
ar
e
b
elo
w
th
e
cu
t
-
o
f
f
p
o
in
t.
T
h
e
lo
w
Fo
u
r
ier
co
ef
f
icien
ts
ar
e
th
e
lin
ea
r
c
o
m
p
o
n
e
n
ts
o
f
th
e
d
ata.
AR
I
M
A,
wh
ich
is
r
ep
u
ted
to
p
er
f
o
r
m
v
er
y
well
o
n
lin
ea
r
tim
e
s
er
ies
d
ata
[
4
]
,
[
1
4
]
is
u
s
ed
to
m
o
d
el
th
e
lin
ea
r
co
m
p
o
n
e
n
t
o
f
th
e
d
ata.
A
h
ig
h
-
p
ass
f
il
ter
is
s
u
b
s
eq
u
en
tly
em
p
lo
y
ed
t
o
o
b
tain
Fo
u
r
ier
c
o
ef
f
icien
ts
ab
o
v
e
th
e
cu
t
-
o
f
f
,
w
h
ich
r
ep
r
esen
t
t
h
e
h
ig
h
Fo
u
r
ie
r
co
ef
f
icien
ts
.
T
h
e
h
ig
h
Fo
u
r
ier
c
o
ef
f
icien
ts
ar
e
n
o
n
lin
ea
r
co
m
p
o
n
e
n
ts
o
f
th
e
d
a
ta.
DL
STM
,
wh
ich
is
v
er
y
ef
f
icien
t
in
m
o
d
elin
g
n
o
n
lin
ea
r
d
ata,
is
u
s
ed
o
n
th
e
n
o
n
lin
ea
r
co
m
p
o
n
e
n
t
th
at
in
cl
u
d
es
th
e
l
o
w
Fo
u
r
ier
c
o
ef
f
icie
n
ts
an
d
t
h
e
r
esid
u
al
er
r
o
r
f
r
o
m
t
h
e
AR
I
MA
m
o
d
eli
n
g
.
T
h
e
r
esu
lts
f
r
o
m
b
o
th
p
ar
t
s
ar
e
co
m
b
in
e
d
to
p
r
o
v
id
e
th
e
f
in
al
p
r
ed
ictio
n
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
lectricity c
o
n
s
u
mp
tio
n
fo
r
ec
a
s
tin
g
u
s
in
g
DF
T d
ec
o
m
p
o
s
itio
n
b
a
s
ed
h
yb
r
id
…
(
Osma
n
Ya
ku
b
u
)
1111
3
.
1
.
Co
nv
er
t
ing
t
he
elec
t
ric
it
y
co
ns
um
ptio
n da
t
a
into
F
o
urier
co
ef
f
icient
s
us
ing
DF
T
DFT
is
th
e
d
is
cr
ete
f
o
r
m
o
f
th
e
Fo
u
r
ier
tr
an
s
f
o
r
m
an
d
co
n
v
e
r
ts
a
s
ig
n
al
o
r
d
is
cr
ete
s
eq
u
en
ce
f
r
o
m
a
r
ep
r
esen
tatio
n
o
f
th
e
tim
e
d
o
m
ain
to
its
r
ep
r
esen
tatio
n
in
t
h
e
Fo
u
r
ier
c
o
ef
f
icien
t
d
o
m
ain
[
3
7
]
.
T
h
e
eq
u
i
v
alen
t
o
f
th
e
co
n
tin
u
o
u
s
F
o
u
r
i
er
tr
a
n
s
f
o
r
m
is
th
e
DFT
f
o
r
s
ig
n
al
s
k
n
o
wn
at
in
s
tan
ts
an
d
s
ep
ar
ated
b
y
s
am
p
le
tim
es,
,
wh
ich
is
a
f
in
ite
d
ata
s
eq
u
en
ce
.
T
h
e
DFT
co
ef
f
icien
ts
ar
e
o
b
tain
ed
as f
o
llo
ws:
[
]
=
∑
[
]
−
2
−
1
=
0
(
1
)
r
ep
r
esen
ts
t
h
e
n
u
m
b
e
r
o
f
o
b
s
er
v
atio
n
s
o
f
th
e
d
ata.
[
]
r
ep
r
esen
ts
th
e
DFT
o
f
t
h
e
s
eq
u
en
ce
[
]
.
T
h
e
(
1
)
c
an
b
e
wr
itten
in
m
atr
ix
f
o
r
m
as:
[
[
0
]
[
1
]
[
2
]
⋮
[
−
1
]
]
=
[
1
1
1
1
…
1
1
2
3
…
−
1
1
2
4
6
…
−
2
1
3
6
9
…
−
3
⋮
1
−
1
−
2
−
3
…
]
[
[
0
]
[
1
]
[
2
]
⋮
[
−
1
]
]
(
2
)
wh
er
e
=
e
xp
(
−
2
)
.
3
.
2
.
Appl
ica
t
io
n o
f
t
he
lo
w
-
pa
s
s
a
nd
hig
h
-
pa
s
s
f
ilte
r
in d
a
t
a
deco
m
po
s
it
io
n
T
h
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
ar
e
co
n
v
er
ted
in
to
Fo
u
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ig
n
als
with
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ier
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ilter
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ig
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with
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t
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ig
h
er
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t
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e
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ar
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n
o
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lin
ea
r
.
T
h
e
lo
w
-
p
ass
f
ilter
is
im
p
lem
e
n
ted
m
ath
em
atica
lly
as
:
̂
(
)
=
{
1
|
|
≤
,
0
|
|
>
,
(
3
)
T
h
e
s
p
ec
if
ied
cu
t
-
o
f
f
Fo
u
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ier
co
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icien
t
is
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en
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.
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h
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am
p
litu
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s
p
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tr
u
m
o
f
th
e
f
ilter
is
th
e
u
n
ity
o
f
|
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<
;
f
u
r
th
e
r
,
f
o
r
h
ig
h
er
F
o
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co
e
f
f
icien
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,
th
e
f
ilter
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as
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am
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s
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tr
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m
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f
z
er
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T
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h
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f
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is
im
p
lem
en
te
d
with
th
e
r
ev
e
r
s
e
o
f
(
3
)
.
3
.
3
.
Appl
ica
t
io
n o
f
I
DF
T
t
o
co
nv
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t
t
he
da
t
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ba
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t
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I
D
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d
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s
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[
]
=
1
∑
[
]
+
2
−
1
=
0
(
4
)
3
.
4
.
M
o
delin
g
t
he
lin
ea
r
co
m
po
nent
wit
h AR
I
M
A
AR
I
MA
is
a
lin
ea
r
m
o
d
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g
tech
n
iq
u
e
wh
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e
th
e
s
p
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cif
ie
d
tim
e
s
er
ies
d
ata
ar
e
ch
ec
k
e
d
f
ir
s
t
f
o
r
s
tatio
n
ar
ity
.
T
im
e
s
er
ies
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
h
av
e
tr
en
d
s
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d
s
ea
s
o
n
ality
,
an
d
,
th
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o
r
e
,
ar
e
n
o
t
s
tatio
n
ar
y
.
W
h
er
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s
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a
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as
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Af
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f
f
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,
if
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till
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ity
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if
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m
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e
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in
ally
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y
.
W
h
en
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e
d
if
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tech
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.
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:
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2
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⋯
−
−
(
5
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wh
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r
ep
r
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m
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el
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d
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alu
es a
r
e
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te
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s
if
=
0
th
en
(
5
)
tu
r
n
s
in
to
an
AR
m
o
d
el
with
th
e
o
r
d
er
Evaluation Warning : The document was created with Spire.PDF for Python.
I
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2
5
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2
I
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J
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Sci,
Vo
l.
24
,
No
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2
,
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er
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if
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(
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MA
m
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with
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s
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itab
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m
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el
o
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(
;
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is
d
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m
in
ed
in
b
u
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in
g
an
AR
I
MA
m
o
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el.
3
.
5
.
Dee
p
lo
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s
ho
rt
-
t
er
m
m
em
o
ry
T
h
e
L
S
T
M
a
r
c
h
i
t
e
c
t
u
r
e
c
o
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p
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i
n
p
u
t
g
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t
e
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c
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a
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e
.
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h
e
f
i
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s
t
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p
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o
d
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c
i
d
e
w
h
i
c
h
i
n
f
o
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m
a
ti
o
n
t
h
e
f
o
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g
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a
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e
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h
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d
t
h
r
o
w
a
wa
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f
r
o
m
t
h
e
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l
s
t
a
t
e
a
n
d
i
s
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e
n
t
e
d
b
y
:
=
(
.
[
ℎ
−
1
,
]
+
)
(
6
)
T
h
e
n
ex
t
s
tag
e
is
to
d
ec
id
e
o
n
th
e
in
f
o
r
m
atio
n
to
b
e
r
etain
e
d
in
th
e
ce
ll
s
tate.
T
h
is
s
tag
e
co
m
p
r
is
es
t
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ts
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th
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in
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u
t
g
ate
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,
wh
ich
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ig
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o
id
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th
e
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alu
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a
n
e
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ate
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wh
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is
cr
ea
ted
b
y
a
ℎ
lay
er
a
n
d
is
ad
d
ed
to
th
e
s
tate.
T
h
is
i
s
m
ath
em
atica
lly
r
ep
r
esen
ted
b
y
:
=
(
.
[
ℎ
−
1
,
]
+
)
(
7
)
̃
=
ℎ
(
.
[
ℎ
−
1
,
]
+
)
(
8
)
T
h
e
p
r
io
r
ce
ll st
ate
−
1
is
u
p
d
ated
in
to
a
n
ew
ce
ll st
ate,
wh
ich
is
r
ep
r
esen
ted
as
:
=
∗
−
1
+
∗
̃
(
9
)
T
h
e
f
in
al
o
u
tp
u
t
is
b
ased
o
n
a
ce
ll
s
tate,
wh
ich
is
a
f
ilter
e
d
v
er
s
io
n
.
T
h
e
c
ell
s
tate
to
b
e
o
u
tp
u
t
is
d
ec
id
ed
b
y
a
s
ig
m
o
id
lay
er
th
at
is
r
u
n
.
DL
STM
is
s
im
ilar
t
o
o
th
e
r
n
e
u
r
al
n
etwo
r
k
s
a
n
d
r
eq
u
ir
es
th
at
d
ata
b
e
with
in
th
e
n
etwo
r
k
’
s
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tiv
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n
f
u
n
ctio
n
.
T
h
e
h
y
p
er
b
o
lic
tan
g
en
t ta
n
h
is
th
e
L
STM
d
ef
au
lt
ac
tiv
atio
n
f
u
n
ctio
n
an
d
th
e
v
al
u
es
o
f
th
e
o
u
t
p
u
t
f
a
ll
b
etwe
en
-
1
an
d
1
,
wh
ich
is
th
e
id
ea
l
r
a
n
g
e
in
th
e
ca
s
e
o
f
tim
e
s
er
ies
d
ata
[
5
]
.
T
h
e
ce
ll
s
tate
is
th
e
n
p
lace
d
t
h
r
o
u
g
h
ℎ
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d
it
p
u
s
h
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th
e
v
alu
es
f
r
o
m
-
1
to
1
,
wh
ich
is
th
en
m
u
ltip
lied
b
y
th
e
o
u
tp
u
t o
f
th
e
s
ig
m
o
id
g
ate,
an
d
th
e
c
o
m
p
o
n
en
t
d
ec
id
ed
o
n
is
o
u
tp
u
t a
s
f
o
llo
ws:
=
(
0
[
ℎ
−
1
,
]
+
0
)
(
1
0
)
ℎ
=
∗
ℎ
(
)
(
1
1
)
Fro
m
(
1
0
)
an
d
(
1
1
)
,
th
e
in
p
u
t
weig
h
t,
r
ec
u
r
r
en
t
weig
h
t,
a
n
d
b
ias
a
r
e
p
r
esen
ted
b
y
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e
L
STM
.
T
o
im
p
r
o
v
e
g
en
e
r
al
p
e
r
f
o
r
m
an
ce
,
an
e
f
f
ec
tiv
e
m
et
h
o
d
is
to
in
c
r
ea
s
e
th
e
d
ep
t
h
o
f
th
e
n
eu
r
al
n
etwo
r
k
[
3
8
]
.
Dee
p
r
ec
u
r
r
en
t
n
etwo
r
k
a
r
ch
itectu
r
es
h
av
e
im
p
r
ess
iv
e
lear
n
in
g
ab
ilit
ies
[
3
9
]
.
I
n
th
e
p
r
o
p
o
s
e
d
DL
STM
,
s
ev
er
al
L
STM
b
lo
ck
s
a
r
e
s
tack
ed
,
as
s
h
o
wn
in
Fig
u
r
e
1
(
b
)
.
T
h
ey
ar
e
co
n
n
ec
ted
i
n
a
d
ee
p
r
ec
u
r
r
e
n
t
n
etwo
r
k
to
d
e
r
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e
th
e
ad
v
an
tag
es
o
f
a
s
in
g
le
L
S
T
M
lay
er
.
T
h
e
p
u
r
p
o
s
e
o
f
s
tack
in
g
m
an
y
L
STM
s
h
ier
ar
ch
i
ca
lly
is
to
b
u
ild
th
e
f
ea
tu
r
es
at
th
e
lo
wer
lay
er
s
f
o
r
th
e
s
ep
ar
atio
n
o
f
th
e
f
ac
t
o
r
s
o
f
v
a
r
iatio
n
s
in
th
e
d
ata
u
s
ed
f
o
r
in
p
u
t
an
d
s
u
b
s
eq
u
en
tly
co
m
b
in
e
th
em
a
t
th
e
h
ig
h
er
lay
e
r
s
.
Su
ch
d
ee
p
ar
ch
itectu
r
e
will
b
etter
g
en
er
alize
b
ec
au
s
e
th
e
r
ep
r
esen
tatio
n
is
m
o
r
e
co
m
p
ac
t th
an
th
e
s
h
allo
w
r
e
p
r
esen
tatio
n
[
4
0
]
.
Fro
m
th
e
ar
c
h
itectu
r
e
in
Fig
u
r
e
1
(
b
)
,
th
e
in
p
u
t
ℎ
is
ass
ig
n
ed
to
L
STM
lay
er
1
at
tim
e
with
ℎ
−
1
,
w
h
ich
is
th
e
p
r
ev
io
u
s
h
id
d
en
s
tate
o
f
th
e
in
itial
L
STM
lay
e
r
,
an
d
tr
an
s
f
er
s
to
th
e
s
ec
o
n
d
lay
er
.
T
h
e
h
id
d
e
n
s
tate
ℎ
is
u
s
ed
b
y
lay
er
2
o
f
t
h
e
L
STM
to
g
eth
e
r
with
th
e
p
r
io
r
h
id
d
en
s
tate
ℎ
−
1
f
o
r
th
e
c
o
m
p
u
t
atio
n
ℎ
o
f
lay
er
2
o
f
th
e
L
STM
a
n
d
m
o
v
es
af
ter
war
d
t
o
th
e
s
u
b
s
eq
u
e
n
t
s
tag
e
u
n
til
th
e
co
m
p
ilatio
n
o
f
t
h
e
last
L
STM
lay
er
.
Par
t
o
f
th
e
task
is
p
r
o
ce
s
s
ed
b
y
ea
ch
lay
e
r
an
d
is
p
ass
ed
to
th
e
n
ex
t
lay
e
r
u
n
til
th
e
last
lay
er
is
r
ea
ch
ed
.
T
o
m
o
d
el
th
e
n
o
n
lin
ea
r
p
a
r
t
o
f
th
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
u
s
in
g
DL
STM
,
th
e
s
eq
u
en
ce
d
ata
ar
e
in
itially
lo
ad
ed
,
w
h
ich
r
esu
lts
in
a
ce
ll a
r
r
ay
,
a
n
d
ea
ch
elem
e
n
t
is
a
s
i
n
g
le
tim
e
s
tep
.
T
h
e
d
ata
ar
e
r
e
s
tr
u
ctu
r
ed
to
a
r
o
w
v
ec
to
r
to
h
av
e
a
m
ea
n
o
f
ze
r
o
an
d
a
u
n
it
v
ar
ian
ce
f
o
r
b
etter
f
itti
n
g
b
y
s
tan
d
ar
d
izin
g
th
e
tr
ai
n
in
g
d
ata.
T
h
e
test
d
ata
ar
e
also
s
tan
d
a
r
d
ized
d
u
r
in
g
th
e
f
o
r
ec
ast
u
s
in
g
th
e
s
am
e
p
ar
am
ete
r
s
as
th
o
s
e
u
s
ed
f
o
r
th
e
tr
ain
in
g
d
ata.
T
h
e
p
r
ed
icto
r
s
an
d
r
esp
o
n
s
es a
r
e
s
u
b
s
eq
u
en
tly
p
r
ep
ar
e
d
.
T
o
p
r
ed
ict
a
s
eq
u
en
ce
’
s
tim
e
s
tep
s
,
th
e
r
esp
o
n
s
es a
r
e
lis
ted
as
th
e
tr
ain
i
n
g
s
eq
u
en
c
e
s
,
an
d
th
e
v
alu
es
ar
e
s
h
if
ted
b
y
a
s
in
g
le
s
tep
.
T
h
e
L
STM
n
e
two
r
k
at
ea
ch
s
tep
o
f
th
e
s
eq
u
e
n
ce
lear
n
s
to
p
r
ed
i
ct
th
e
s
u
b
s
eq
u
en
t
v
alu
e
o
f
th
e
tim
e
s
tep
.
T
h
er
ef
o
r
e
,
th
e
p
r
ed
i
cto
r
is
th
e
tr
ain
in
g
s
eq
u
en
ce
with
o
u
t th
e
last
s
tep
.
4.
E
XP
E
R
I
M
E
N
T
A
L
SE
T
UP
T
h
e
ex
p
e
r
im
en
tal
s
ettin
g
s
th
a
t
wer
e
im
p
lem
e
n
ted
f
o
r
b
o
th
th
e
p
r
o
p
o
s
ed
an
d
r
e
f
er
en
ce
m
o
d
els
ar
e
p
r
esen
ted
in
th
is
s
ec
tio
n
.
A
b
r
ief
o
v
er
v
iew
o
f
th
e
r
e
f
er
en
ce
m
o
d
els
an
d
th
e
id
ea
l
cr
iter
ia
to
b
e
r
elied
o
n
f
o
r
co
m
p
ar
in
g
th
eir
p
er
f
o
r
m
an
ce
ag
ain
s
t th
e
p
r
o
p
o
s
ed
m
o
d
el
ar
e
also
p
r
esen
ted
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
lectricity c
o
n
s
u
mp
tio
n
fo
r
ec
a
s
tin
g
u
s
in
g
DF
T d
ec
o
m
p
o
s
itio
n
b
a
s
ed
h
yb
r
id
…
(
Osma
n
Ya
ku
b
u
)
1113
4
.
1
.
H
y
brid ARIM
A
–
D
L
S
T
M
predict
io
n m
o
del
AR
I
MA
i
s
u
s
ed
to
m
o
d
el
th
e
r
ec
o
n
s
tr
u
cted
lin
ea
r
p
a
r
t
o
f
th
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata;
th
e
r
esid
u
als
an
d
th
e
n
o
n
lin
ea
r
p
ar
t
ar
e
m
o
d
eled
u
s
in
g
DL
ST
M.
T
h
e
g
en
er
ated
p
r
e
d
ictio
n
s
f
r
o
m
AR
I
MA
an
d
DL
STM
ar
e
ag
g
r
eg
ated
to
att
ain
th
e
to
tal
f
o
r
ec
ast.
T
h
e
tim
e
s
er
ies
d
en
o
ted
,
co
m
p
r
is
ed
lin
ea
r
(
lo
w)
an
d
n
o
n
lin
ea
r
(
h
ig
h
)
Fo
u
r
ie
r
co
ef
f
icien
ts
,
wh
ich
is
:
=
+
(
1
2
)
r
ep
r
esen
ts
th
e
n
o
n
lin
ea
r
(
h
ig
h
)
Fo
u
r
ier
co
ef
f
icie
n
t
p
ar
t
an
d
r
ep
r
esen
ts
th
e
lin
ea
r
(
lo
w)
F
o
u
r
ier
co
ef
f
icien
t
p
ar
t.
is
m
ad
e
s
tati
o
n
ar
y
as
a
lin
ea
r
f
u
n
ctio
n
,
an
d
,
as
s
h
o
wn
in
(
1
3
)
,
m
o
d
eled
u
s
in
g
AR
I
MA
.
is
ex
p
r
ess
ed
as a
n
o
n
lin
ea
r
f
u
n
ctio
n
,
an
d
DL
STM
is
u
s
ed
f
o
r
its
m
o
d
elin
g
,
as sh
o
wn
in
(
1
4
)
.
̂
=
(
−
1
,
−
2
,
…
…
)
(
1
3
)
̂
=
(
−
1
,
−
2
,
…
,
−
)
+
(
1
4
)
s
i
g
n
i
f
i
e
s
t
h
e
n
o
n
l
i
n
e
a
r
f
u
n
c
t
i
o
n
a
n
d
s
i
g
n
i
f
i
e
s
t
h
e
m
o
d
e
l
e
r
r
o
r
.
T
h
e
f
o
r
e
c
a
s
t
v
a
l
u
e
̂
i
s
s
h
o
w
n
i
n
(
1
5
)
:
̂
=
̂
+
̂
(
1
5
)
I
n
s
elec
tin
g
th
e
b
est
f
it
m
o
d
el
in
AR
I
MA
,
th
e
ak
aik
e
in
f
o
r
m
atio
n
c
r
iter
io
n
(
A
I
C
)
is
u
s
ed
,
wh
ich
s
u
g
g
ests
th
at
th
e
b
est
m
o
d
el
i
s
AR
I
MA
(
7
,
0
,
0
)
.
T
h
e
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
ar
e
d
i
v
id
ed
in
to
7
0
%
f
o
r
tr
ain
in
g
an
d
3
0
%
f
o
r
test
in
g
,
a
n
d
b
ec
au
s
e
o
n
ly
th
e
n
ex
t d
ay
’
s
f
o
r
ec
ast
is
d
esire
d
,
o
n
e
-
s
tep
-
ah
ea
d
p
r
e
d
ictio
n
is
em
p
lo
y
ed
.
T
h
e
L
STM
n
etwo
r
k
ar
ch
itectu
r
e
is
th
en
d
ef
in
e
d
b
y
co
n
s
tr
u
ctin
g
an
L
STM
r
eg
r
ess
io
n
n
etwo
r
k
.
T
h
e
n
etwo
r
k
s
tr
u
ctu
r
e
is
[
A,
B
,
C
,
D]
.
A
r
ep
r
esen
ts
th
e
in
p
u
t
lay
er
,
its
s
ize
i
s
d
en
o
ted
b
y
B
,
wh
ich
f
ee
d
s
in
to
an
L
STM
lay
e
r
with
B
n
eu
r
o
n
s
,
wh
ich
s
u
b
s
e
q
u
en
tly
f
ee
d
s
in
to
an
o
th
er
lay
er
o
f
L
STM
with
C
n
eu
r
o
n
s
a
n
d
th
en
f
ee
d
s
in
to
a
n
o
r
m
al
lay
e
r
o
f
D
n
eu
r
o
n
s
th
at
is
f
u
lly
c
o
n
n
ec
ted
t
o
a
lin
ea
r
ac
tiv
atio
n
th
at
is
u
s
ed
in
th
e
s
u
b
s
eq
u
en
t
s
tep
’
s
f
o
r
ec
ast.
T
o
p
r
ev
en
t
g
r
ad
ien
t
ex
p
lo
s
io
n
,
t
h
e
th
r
esh
o
ld
o
f
th
e
g
r
a
d
i
en
t
is
s
et
to
1
.
Af
ter
th
e
L
STM
n
etwo
r
k
is
tr
ain
ed
with
th
e
tr
ain
in
g
o
p
ti
o
n
s
in
d
ica
ted
,
th
e
tim
e
s
tep
s
f
o
r
th
e
f
u
tu
r
e
ar
e
p
r
ed
icted
in
d
iv
id
u
ally
,
an
d
th
e
s
tate
o
f
t
h
e
n
etwo
r
k
is
u
p
d
ated
f
o
r
ea
c
h
f
o
r
ec
ast.
T
h
e
p
r
io
r
f
o
r
e
ca
s
t
is
u
s
ed
as
an
in
p
u
t
f
u
n
ctio
n
i
n
f
o
r
ec
asti
n
g
f
u
tu
r
e
s
tep
s
.
4
.
2
.
Re
f
er
ence
m
o
dels
T
o
ac
h
ie
v
e
a
f
air
ev
alu
atio
n
,
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
AR
I
MA
–
DL
STM
m
o
d
el
b
ased
o
n
DFT
d
ec
o
m
p
o
s
itio
n
is
co
m
p
ar
ed
a
g
ain
s
t
r
ef
er
en
ce
m
o
d
els,
wh
ic
h
ar
e
s
in
g
le
s
tatis
tical
o
r
s
in
g
le
m
ac
h
in
e
lear
n
i
n
g
m
o
d
els,
an
d
h
y
b
r
id
s
tatis
tical
an
d
m
ac
h
in
e
lear
n
i
n
g
m
o
d
els.
T
h
e
r
e
f
er
en
ce
m
o
d
els
ar
e
s
elec
ted
b
ased
o
n
th
e
im
p
ac
t
f
ac
to
r
o
f
th
e
j
o
u
r
n
als
in
wh
ich
th
e
y
ar
e
p
u
b
lis
h
ed
,
t
h
eir
citatio
n
s
,
an
d
t
h
e
citatio
n
s
o
f
th
e
au
th
o
r
s
in
s
im
ilar
wo
r
k
u
n
d
er
tak
en
in
o
t
h
er
p
ap
er
s
,
th
e
q
u
ality
o
f
m
o
d
els
th
ey
wer
e
c
o
m
p
ar
e
d
wit
h
,
an
d
t
h
eir
y
ea
r
o
f
p
u
b
licatio
n
.
T
h
e
r
ef
e
r
en
ce
m
o
d
els u
s
ed
ar
e
as f
o
llo
ws:
4
.
2
.
1
.
ARIM
A
m
o
del
T
h
e
co
n
ce
p
t
o
f
t
h
e
AR
I
MA
m
o
d
el
is
ex
p
lain
ed
in
s
ec
tio
n
2
.
T
h
e
AR
I
MA
c
o
m
p
ar
is
o
n
s
ig
n
if
ies
a
s
tatis
t
ical
co
m
p
ar
is
o
n
.
T
h
e
s
tats
m
o
d
el
lib
r
ar
y
in
Py
th
o
n
was
u
s
ed
to
im
p
lem
en
t
th
e
AR
I
MA
p
r
o
g
r
am
.
A
g
r
id
s
ea
r
ch
th
at
ex
p
lo
r
es d
iv
er
s
e
c
o
m
b
in
atio
n
s
o
f
th
e
id
e
n
tifie
d
p
ar
am
eter
s
(
p
,
d
,
q
)
is
u
s
ed
.
A
n
ew
AR
I
MA
m
o
d
el
is
f
it
f
o
r
ea
ch
p
ar
am
eter
co
m
b
in
atio
n
an
d
th
e
AI
C
is
th
en
u
s
ed
to
s
elec
t
th
e
b
est
co
m
b
in
atio
n
.
T
h
e
AI
C
m
ea
s
u
r
es h
o
w
well
th
e
m
o
d
el
f
its
th
e
d
ata,
co
n
s
id
er
in
g
th
e
o
v
er
all
co
m
p
lex
it
y
o
f
t
h
e
m
o
d
e
l.
4
.
2
.
2
.
H
y
brid E
T
S
-
ANN
m
o
del f
o
r
t
im
e
s
er
ies
f
o
re
ca
s
t
in
g
[
1
4
]
T
h
is
m
o
d
el
e
n
s
u
r
es
th
at
p
u
r
e
ly
lin
ea
r
,
p
u
r
el
y
n
o
n
lin
ea
r
,
o
r
a
co
m
b
in
atio
n
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
ar
e
m
o
d
eled
ac
c
u
r
ately
.
I
n
th
eir
m
et
h
o
d
,
th
e
E
T
S
is
in
itial
ly
ap
p
lied
to
th
e
tim
e
s
er
ies
d
ata.
T
h
is
in
cr
ea
s
es
th
e
ch
an
ce
s
o
f
f
in
d
in
g
lin
ea
r
p
atter
n
s
wh
er
e
t
h
ey
ex
is
t.
T
o
ca
lcu
late
th
e
r
esid
u
al
er
r
o
r
,
th
e
p
r
ed
ictio
n
s
f
r
o
m
th
e
E
T
S
m
o
d
el
ar
e
d
ed
u
ce
d
f
r
o
m
th
e
o
r
i
g
in
al
s
er
ies.
ANN
is
u
s
ed
to
m
o
d
el
th
e
r
esid
u
al
er
r
o
r
s
eq
u
en
ce
,
wh
ich
is
ass
u
m
ed
to
b
e
n
o
n
lin
ea
r
.
T
h
e
f
in
a
l
p
r
ed
ictio
n
s
ar
e
o
b
tain
ed
th
r
o
u
g
h
a
co
m
b
in
atio
n
o
f
th
e
p
r
ed
ictio
n
s
f
r
o
m
th
e
E
T
S a
n
d
ANN.
4
.
2
.
3
.
M
o
delin
g
a
nd
predict
i
o
n o
f
T
urk
ey
’
s
elec
t
ricit
y
co
ns
um
ptio
n us
ing
ANN
[
1
0
]
An
ML
P
n
eu
r
al
n
etwo
r
k
to
p
o
lo
g
y
an
d
a
b
ac
k
p
r
o
p
a
g
atio
n
tr
ain
in
g
alg
o
r
ith
m
ar
e
u
s
ed
in
t
h
is
m
o
d
el.
T
an
g
en
t
-
s
ig
m
o
i
d
an
d
p
u
r
e
-
lin
ea
r
d
ata
r
esp
ec
tiv
ely
ar
e
s
ele
cted
in
th
e
h
id
d
en
an
d
o
u
tp
u
t
lay
er
p
r
o
ce
s
s
in
g
elem
en
ts
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
5
0
2
-
4
7
5
2
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci,
Vo
l.
24
,
No
.
2
,
No
v
em
b
er
2
0
2
1
:
1
1
0
7
-
1
1
2
0
1114
4
.
2
.
4
.
E
lect
ricit
y
co
ns
um
ptio
n pre
dict
io
n ba
s
e
d
o
n L
S
T
M
wit
h a
t
t
ent
io
n m
ec
ha
nis
m
[
2
1
]
I
n
th
is
wo
r
k
,
a
n
L
STM
with
an
atten
tio
n
m
ec
h
an
is
m
i
s
p
r
esen
ted
f
o
r
s
h
o
r
t
-
ter
m
t
im
e
-
p
h
ase
elec
tr
icity
co
n
s
u
m
p
tio
n
m
o
d
e
lin
g
.
T
h
e
atten
tio
n
m
ec
h
an
is
m
is
in
itially
u
s
ed
to
allo
ca
te
co
ef
f
icien
ts
to
th
e
s
eq
u
en
ce
d
ata
o
f
th
e
in
p
u
t.
T
h
e
v
al
u
e
o
f
th
e
o
u
tp
u
t
o
f
e
ac
h
L
STM
ce
ll
is
ca
lc
u
lated
u
s
in
g
th
e
f
o
r
war
d
p
r
o
p
a
g
atio
n
m
eth
o
d
.
T
h
e
b
a
ck
p
r
o
p
ag
atio
n
m
eth
o
d
is
u
s
ed
to
co
m
p
u
te
th
e
er
r
o
r
b
etw
ee
n
th
e
ac
tu
al
an
d
p
r
ed
icted
v
alu
es.
E
ac
h
g
r
ad
ie
n
t’
s
weig
h
t
is
co
m
p
u
ted
in
ac
co
r
d
an
ce
with
th
e
c
o
r
r
esp
o
n
d
i
n
g
er
r
o
r
ter
m
,
an
d
,
to
r
ed
u
ce
t
h
e
er
r
o
r
,
th
e
m
o
d
el’
s
weig
h
t is u
p
d
ated
b
y
th
e
g
r
a
d
ien
t d
escen
t d
ir
ec
tio
n
.
4
.
2
.
5
.
A
hy
brid
predict
io
n
mo
del
f
o
r
re
s
identia
l
elec
t
ricit
y
co
ns
um
ptio
n
us
ing
H
o
lt
–
Winte
rs
a
n
d
ex
t
re
m
e
le
a
rning
m
a
chine
[
1
5
]
A
h
y
b
r
id
m
o
d
el
b
ased
o
n
th
e
h
o
lt
-
win
ter
s
(
HW
)
m
eth
o
d
a
n
d
a
n
E
L
M
n
etwo
r
k
ar
e
u
s
ed
to
p
r
ed
ict
r
esid
en
tial
elec
tr
icity
co
n
s
u
m
p
tio
n
in
th
e
s
h
o
r
t
ter
m
.
An
M
A
f
ilter
is
u
s
ed
to
d
ec
o
m
p
o
s
e
th
e
o
r
ig
i
n
al
d
ata
in
co
m
p
o
n
en
ts
o
f
a
s
tatio
n
ar
y
li
n
ea
r
an
d
f
lu
ct
u
an
t
n
o
n
lin
ea
r
r
esid
u
al.
T
h
e
lin
ea
r
p
r
e
d
ictio
n
m
o
d
el
is
g
en
e
r
ated
b
y
th
e
HW
m
eth
o
d
an
d
is
u
s
ed
to
p
r
ed
ict
th
e
lin
ea
r
co
m
p
o
n
en
t.
T
h
e
E
L
M
b
u
ild
s
a
n
o
n
lin
ea
r
m
o
d
el
f
o
r
p
r
ed
ictin
g
r
esid
e
n
tial
elec
tr
icity
co
n
s
u
m
p
tio
n
b
y
u
s
in
g
lin
ea
r
f
o
r
e
ca
s
t
r
esu
lts
,
n
o
n
lin
ea
r
r
esid
u
als,
an
d
o
r
ig
in
al
d
ata
as in
p
u
ts
.
4
.
2
.
6
.
F
a
ce
bo
o
k
’
s
P
ro
ph
et
Pro
p
h
et
is
a
d
ec
o
m
p
o
s
ab
l
e
ti
m
e
s
er
ies
m
o
d
el
th
at
h
as
th
r
ee
m
o
d
el
p
a
r
ts
:
tr
en
d
,
s
ea
s
o
n
ality
,
an
d
h
o
lid
ay
s
.
T
h
e
y
ar
e
r
ep
r
esen
ted
as f
o
llo
ws:
(
)
=
(
)
+
(
)
+
ℎ
(
)
+
(
1
6
)
wh
er
e
(
)
d
en
o
tes
th
e
tr
en
d
f
u
n
ct
io
n
f
o
r
m
o
d
elin
g
n
o
n
-
p
er
io
d
ic
ch
an
g
es
in
th
e
v
alu
e
tim
e
s
er
i
es,
(
)
is
th
e
p
er
io
d
ic
c
h
an
g
e
(
i.e
.
,
s
ea
s
o
n
ality
)
,
ℎ
(
)
d
en
o
tes
th
e
ef
f
ec
t o
f
h
o
li
d
ay
s
th
at
o
cc
u
r
with
ir
r
eg
u
lar
s
ch
ed
u
les,
an
d
r
ep
r
esen
ts
th
e
e
r
r
o
r
ter
m
th
at
ac
co
u
n
t
s
f
o
r
a
n
y
u
n
co
m
m
o
n
ch
a
n
g
es
th
at
a
r
e
n
o
t
ac
co
m
m
o
d
ated
b
y
th
e
m
o
d
el.
4
.
3
.
M
ea
s
urem
ent
o
f
mo
del pre
dict
io
n per
f
o
rm
a
nce
T
o
m
ea
s
u
r
e
th
e
p
er
f
o
r
m
an
ce
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
a
n
d
c
o
m
p
ar
e
it
ag
ai
n
s
t
th
e
r
ef
er
en
ce
m
o
d
els;
R
MSE
,
MA
PE,
an
d
MA
E
r
ep
u
ted
to
b
e
ef
f
ec
tiv
e
in
m
ea
s
u
r
in
g
p
r
e
d
ictio
n
er
r
o
r
s
[
4
1
]
ar
e
co
m
p
u
ted
.
T
h
e
R
MSE
m
ea
s
u
r
es th
e
er
r
o
r
b
etwe
en
th
e
p
r
ed
icted
a
n
d
o
b
s
er
v
ed
v
alu
es.
T
h
e
s
m
aller
th
e
er
r
o
r
,
th
e
b
etter
will b
e
th
e
p
r
ed
ictio
n
.
R
MSE
is
co
m
p
u
ted
as f
o
llo
ws:
=
√
∑
(
−
)
2
=
1
(
1
7
)
T
h
e
MA
PE
u
s
u
ally
ex
p
r
ess
ed
as a
p
er
ce
n
tag
e
g
en
er
ally
s
tate
s
th
e
ac
cu
r
ac
y
o
f
p
r
ed
ictio
n
as
a
r
atio
an
d
is
d
ef
in
e
d
b
y
th
e
f
o
r
m
u
la:
M
A
PE
=
1
∑
|
−
=
1
|
∗
100
(
1
8
)
T
h
e
MA
E
is
s
im
p
ly
an
av
e
r
ag
e
o
f
th
e
a
b
s
o
lu
te
p
er
ce
n
tag
e
er
r
o
r
s
b
etwe
en
th
e
ac
t
u
al
an
d
p
r
ed
icted
v
alu
es a
n
d
is
co
m
p
u
te
d
as f
o
llo
ws:
=
∑
|
−
|
=
1
(
1
9
)
wh
er
e
d
en
o
tes
th
e
v
alu
e
p
r
ed
icted
,
th
e
o
b
s
er
v
ed
v
alu
es
at
tim
e
ar
e
d
en
o
ted
b
y
,
an
d
th
e
n
u
m
b
er
o
f
tim
e
elem
en
ts
is
d
en
o
ted
b
y
.
5.
RE
SU
L
T
S
A
ND
D
IS
CU
SS
I
O
N
E
lectr
icity
co
n
s
u
m
p
tio
n
d
ata
h
av
e
tr
en
d
s
an
d
s
ea
s
o
n
ality
an
d
,
th
er
e
f
o
r
e,
a
r
e
co
m
p
o
s
ed
o
f
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
.
DFT
co
n
v
er
ts
th
e
d
ata
in
to
Fo
u
r
ie
r
co
ef
f
icien
ts
,
an
d
,
b
ased
o
n
a
cu
t
-
o
f
f
Fo
u
r
ier
co
ef
f
icien
t,
l
o
w
-
p
ass
an
d
h
i
g
h
-
p
ass
f
ilter
s
ar
e
u
s
ed
t
o
d
ec
o
m
p
o
s
e
th
e
d
ata
in
to
lin
ea
r
an
d
n
o
n
lin
ea
r
co
m
p
o
n
en
ts
.
T
h
e
Fo
u
r
ier
co
e
f
f
icien
ts
ar
e
co
n
v
er
ted
b
ac
k
in
to
th
eir
o
r
ig
in
al
f
o
r
m
s
u
s
in
g
in
v
er
s
e
d
is
cr
ete
Fo
u
r
ier
tr
a
n
s
f
o
r
m
(
I
DFT)
.
T
h
e
lin
ea
r
c
o
m
p
o
n
en
t
is
m
o
d
el
ed
b
y
AR
I
MA
,
an
d
th
e
n
o
n
li
n
ea
r
co
m
p
o
n
en
t
is
mode
led
b
y
DL
STM
,
wh
ich
h
as
th
e
ca
p
ab
ilit
y
o
f
m
o
d
e
lin
g
n
o
n
lin
ea
r
d
ata
v
er
y
ac
c
u
r
ately
.
Ho
u
s
eh
o
l
d
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ata
g
ath
er
ed
in
Fra
n
ce
e
v
er
y
m
in
u
te
f
o
r
4
7
m
o
n
th
s
f
r
o
m
Dec
em
b
er
2
0
0
6
t
o
Evaluation Warning : The document was created with Spire.PDF for Python.
I
n
d
o
n
esian
J
E
lec
E
n
g
&
C
o
m
p
Sci
I
SS
N:
2502
-
4
7
5
2
E
lectricity c
o
n
s
u
mp
tio
n
fo
r
ec
a
s
tin
g
u
s
in
g
DF
T d
ec
o
m
p
o
s
itio
n
b
a
s
ed
h
yb
r
id
…
(
Osma
n
Ya
ku
b
u
)
1115
No
v
em
b
er
2
0
1
0
,
r
ep
r
esen
tin
g
2
,
0
7
5
,
2
5
9
p
o
wer
m
ea
s
u
r
em
e
n
ts
[
4
2
]
,
ar
e
u
s
ed
in
th
e
ev
alu
atio
n
o
f
th
e
m
o
d
el.
T
o
en
s
u
r
e
ac
c
u
r
ate
p
r
ed
ictio
n
s
,
th
e
d
ata
wer
e
ag
g
r
e
g
ated
d
aily
an
d
u
s
ed
f
o
r
th
e
f
o
r
ec
ast.
T
h
e
q
u
an
titativ
e
an
d
v
is
u
al
r
esu
l
ts
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
AR
I
MA
-
DL
STM
m
o
d
el
alo
n
g
with
th
e
r
ef
er
en
ce
m
o
d
els
ar
e
p
r
esen
ted
in
th
is
s
ec
tio
n
.
T
h
e
in
d
iv
id
u
al
h
o
u
s
eh
o
ld
elec
tr
icity
co
n
s
u
m
p
tio
n
d
ataset
is
u
s
ed
f
o
r
th
e
p
r
o
p
o
s
ed
an
d
r
ef
er
en
ce
m
o
d
els.
T
h
is
d
ataset
r
ep
r
esen
ts
2
,
0
7
5
,
2
5
9
p
o
we
r
m
ea
s
u
r
em
e
n
ts
co
llected
in
a
h
o
u
s
e
s
itu
ated
in
Scea
u
x
n
ea
r
Par
is
,
Fra
n
ce
,
f
o
r
4
7
m
o
n
th
s
s
p
an
n
in
g
Dec
e
m
b
er
2
0
0
6
to
No
v
em
b
er
2
0
1
0
with
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