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I
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N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
201
9
:
3
1
7
–
327
318
in
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im
e
Ser
ie
s
f
o
cu
s
e
s
o
n
a
s
in
g
le
v
ar
iab
le
th
at
is
o
b
s
er
v
ed
in
d
if
f
er
e
n
t
p
er
io
d
s
.
A
ti
m
e
s
er
ies
is
th
e
r
esu
ltan
t o
f
d
if
f
er
en
t c
o
m
p
o
n
en
t
s
n
a
m
el
y
:
T
r
en
d
:
ev
o
lu
ti
o
n
o
f
th
e
s
e
r
ies
i
n
th
e
lo
n
g
te
r
m
.
r
eg
u
la
r
tim
e
in
te
r
v
al
.
R
esid
u
a
l
(
n
o
is
e
)
:
i
r
r
eg
u
lar
v
a
r
i
ati
o
n
in
a
tim
e
in
te
r
v
a
l.
2
.
1
.
1.
ARIM
A
A
R
I
MA
s
tan
d
s
f
o
r
A
u
to
r
eg
r
e
s
s
iv
e
(
A
R
)
I
n
t
eg
r
ate
d
(
I
)
M
o
v
in
g
Av
er
ag
e
(
MA
)
,
als
o
k
n
o
w
n
as
th
e
B
o
x
-
J
en
k
in
s
a
p
p
r
o
ac
h
.
A
n
A
R
I
MA
m
o
d
el
is
s
p
ec
if
ie
d
b
y
th
e
3
p
ar
am
eter
s
(
p
,
d
,
q
)
,
s
u
ch
a
s
:
p
is
th
e
n
u
m
b
er
o
f
a
u
to
r
eg
r
es
s
iv
e
ter
m
s
[
A
R
(
p
)
]
d
is
th
e
n
u
m
b
er
o
f
d
i
f
f
er
en
tiat
i
o
n
[
I
(
d
)
]
q
is
th
e
n
u
m
b
er
o
f
m
o
v
in
g
av
e
r
ag
es [
M
A
(
q
)
]
A
s
eq
u
en
ce
{
Xt
,
ti
∈
T
}
is
ca
lled
AR
I
M
A
p
r
o
ce
s
s
o
f
o
r
d
er
(
p
,
d
,
q
)
A
R
I
MA
(
p
,
d
,
q
)
if
it
ca
n
b
e
w
r
it
ten
i
n
th
e
f
o
llo
w
i
n
g
f
o
r
m
u
la
:
2
.
1
.
2
.
B
ox
-
j
enk
ins
Fig
u
r
e
1
s
h
o
w
s
t
h
e
B
o
x
-
J
e
n
k
i
n
s
m
et
h
o
d
[
3
]
s
u
m
m
ar
izes th
e
AR
I
M
A
p
r
o
ce
s
s
in
t
h
r
ee
m
ai
n
s
tep
s
:
I
d
en
tif
icat
io
n
:
T
h
is
f
ir
s
t
s
tep
is
to
b
r
ea
k
d
o
w
n
t
h
e
ti
m
e
s
er
ies
ac
co
r
d
in
g
to
t
h
e
t
h
r
ee
p
r
o
ce
s
s
es:
A
R
(
au
to
r
eg
r
ess
i
v
e)
,
I
(
in
te
g
r
ated
)
an
d
M
A
(
m
o
v
i
n
g
a
v
er
a
g
e)
.
T
h
is
s
tep
o
b
v
io
u
s
l
y
m
ak
e
s
i
t
p
o
s
s
ib
le
to
s
p
ec
if
y
t
h
e
p
ar
a
m
eter
s
p
,
d
an
d
q
,
w
h
ile
f
ir
s
t
ch
ec
k
i
n
g
t
h
e
s
t
atio
n
ar
it
y
o
f
t
h
e
s
er
ies.
Sp
ec
if
icatio
n
o
f
th
e
p
ar
am
eter
s
p
,
q
is
d
o
n
e
th
an
k
s
to
th
e
au
to
co
r
r
elatio
n
f
u
n
cti
o
n
s
an
d
t
h
e
p
ar
tial
au
to
co
r
r
elatio
n
w
h
ich
w
e
w
il
l d
is
cu
s
s
i
n
d
etail
i
n
th
e
r
ea
lizatio
n
p
ar
t.
T
h
e
p
ar
am
eter
d
is
th
e
o
r
d
er
o
f
d
if
f
er
e
n
tiatio
n
.
E
s
ti
m
a
tio
n
:
T
h
e
s
ec
o
n
d
s
tep
o
f
t
h
e
B
o
x
-
J
en
k
in
s
p
r
o
ce
d
u
r
e
is
to
esti
m
ate
th
e
p
ar
a
m
eter
s
o
f
t
h
e
ap
p
r
o
p
r
iate
m
o
d
els b
y
p
r
o
v
id
i
n
g
t
h
e
o
r
d
er
s
p
,
d
an
d
q
.
th
e
esti
m
atio
n
is
d
o
n
e
u
s
i
n
g
n
o
n
-
li
n
ea
r
m
e
th
o
d
s
.
Diag
n
o
s
is
:
T
h
e
last
s
tep
o
f
t
h
e
B
o
x
-
J
e
n
k
i
n
s
m
e
th
o
d
co
n
c
er
n
s
t
h
e
v
er
if
ica
t
io
n
o
f
th
e
r
elev
an
ce
o
f
t
h
e
m
o
d
el.
T
h
at
is
,
to
v
er
if
y
t
h
at
th
e
esti
m
ated
m
o
d
el
is
ad
ap
ted
to
th
e
d
ata
av
ailab
le.
T
o
d
o
t
h
is
w
e
r
ef
er
to
s
tatis
t
ical
test
s
.
Fig
u
r
e
1
.
B
o
x
j
en
k
in
s
2
.
1
.
3
.
Ra
nd
o
m
w
a
lk
R
an
d
o
m
w
a
lk
ar
e
s
to
c
h
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ic
p
r
o
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s
s
es
f
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ed
b
y
s
u
cc
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s
s
iv
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s
u
m
m
atio
n
o
f
i
n
d
ep
en
d
en
t,
id
en
ticall
y
d
is
tr
ib
u
ted
r
an
d
o
m
v
ar
iab
les
[
4
]
.
I
n
t
h
e
ar
i
m
a
m
o
d
els,
r
an
d
o
m
w
al
k
co
r
r
esp
o
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d
s
to
t
h
e
AR
I
M
A
m
o
d
e
l (
0
,
1
,
0
)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
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N:
2252
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o
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ec
a
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r
a
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d
o
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vs LS
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r
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Ma
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319
2
.
2
.
Dee
p
lea
rning
Dee
p
L
ea
r
n
in
g
[
5
]
i
s
a
s
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b
f
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ac
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lear
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o
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m
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tio
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b
ef
o
r
e
th
e
y
ar
e
o
u
tp
u
t.
2
.
2
.
1
.
Neura
l
net
wo
rk
An
ar
ti
f
icia
l
n
eu
r
al
n
e
t
w
o
r
k
i
s
in
s
p
ir
ed
b
y
t
h
e
f
u
n
ctio
n
i
n
g
o
f
b
io
lo
g
ical
n
e
u
r
o
n
s
.
W
r
itte
n
i
n
t
h
e
f
o
r
m
o
f
an
alg
o
r
it
h
m
,
t
h
e
n
e
u
r
al
n
et
w
o
r
k
ca
n
m
o
d
if
y
it
s
elf
ac
co
r
d
in
g
to
t
h
e
r
esu
lt
s
o
f
its
ac
tio
n
s
,
w
h
ich
allo
w
s
i
t
to
lear
n
an
d
s
o
l
v
e
p
r
o
b
lem
s
w
it
h
o
u
t
h
u
m
a
n
i
n
ter
v
e
n
tio
n
.
A
n
eu
r
al
n
et
w
o
r
k
co
n
s
i
s
ts
o
f
th
r
ee
p
ar
ts
,
an
in
p
u
t
la
y
er
,
h
id
d
en
la
y
er
s
,
a
n
d
an
o
u
tp
u
t
la
y
er
.
T
h
e
in
p
u
t
la
y
er
s
a
r
e
a
s
er
ies
o
f
n
eu
r
o
n
s
co
n
tai
n
i
n
g
t
h
e
in
p
u
t
s
i
g
n
al
th
at
w
i
ll
b
e
tr
an
s
m
i
tted
to
th
e
h
id
d
en
la
y
er
s
,
t
h
ese
la
y
er
s
r
ep
r
esen
t
t
h
e
h
ea
r
t
o
f
t
h
e
n
eu
r
al
n
et
w
o
r
k
it
is
at
th
i
s
lev
el
w
h
er
e
t
h
e
r
elatio
n
s
b
etw
ee
n
t
h
e
d
if
f
er
e
n
t
v
ar
iab
le
s
a
r
e
h
ig
h
li
g
h
ted
.
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h
e
en
d
r
esu
l
t
,
o
f
ten
a
p
r
ed
ictio
n
r
esu
lt,
is
at
t
h
e
o
u
tp
u
t la
y
er
.
2
.
2
.
2
.
Rec
urre
nt
neura
l net
wo
rk
(
RNN)
A
r
ec
u
r
r
en
t
n
eu
r
al
n
et
w
o
r
k
o
p
er
ates
f
r
o
m
s
eq
u
e
n
tial
d
at
a,
an
d
lear
n
s
f
r
o
m
t
h
e
s
u
cc
ess
io
n
o
f
p
r
ev
io
u
s
s
ta
tes.
E
ac
h
o
u
tp
u
t
d
ep
en
d
s
o
n
th
e
ca
lc
u
latio
n
d
o
n
e
d
o
w
n
s
tr
ea
m
.
I
n
p
r
in
cip
le,
R
NNs
ca
n
lear
n
to
m
ap
o
n
e
v
ar
iab
le
s
eq
u
e
n
ce
to
an
o
t
h
er
.
R
NN
s
ar
e
eq
u
i
v
alen
t
to
v
er
y
d
ee
p
n
eu
r
al
n
et
w
o
r
k
s
t
h
at
s
h
ar
e
m
o
d
el
p
ar
am
eter
s
an
d
r
ec
eiv
e
in
p
u
t
at
ea
ch
tim
e
s
tep
.
A
n
R
NN
is
ess
en
tia
ll
y
c
h
ar
ac
ter
ized
b
y
t
h
e
f
ac
t
th
a
t
it
co
n
tain
s
at
least
o
n
e
r
etu
r
n
co
n
n
ec
t
io
n
s
o
th
a
t
t
h
e
ac
ti
v
atio
n
s
cir
cu
la
te
i
n
lo
o
p
s
.
R
ec
u
r
s
io
n
at
th
e
h
id
d
en
la
y
er
o
f
R
N
Ns
ca
n
ac
t
a
s
a
m
e
m
o
r
y
m
e
c
h
a
n
is
m
f
o
r
n
e
t
w
o
r
k
s
(
b
ec
au
s
e
t
h
e
o
u
tp
u
t
at
ti
m
e
t
is
a
f
u
n
ctio
n
o
f
all
p
r
ev
io
u
s
i
n
p
u
t
s
)
.
A
t
ea
ch
ti
m
e
s
tep
,
th
e
lear
n
ed
r
ec
u
r
s
io
n
w
e
ig
h
ts
ca
n
d
ec
id
e
w
h
ic
h
i
n
f
o
r
m
atio
n
to
f
o
r
g
e
t
an
d
w
h
ic
h
o
n
e
s
to
k
ee
p
in
o
r
d
er
to
r
ela
y
t
h
e
m
o
v
er
ti
m
e.
Am
o
n
g
t
h
e
m
ai
n
p
r
o
b
le
m
s
o
f
a
n
R
NN,
u
n
j
u
s
ti
f
ied
a
m
p
li
f
icatio
n
o
f
w
eig
h
t
s
an
d
th
e
m
o
d
el
b
ein
g
u
n
ab
le
to
le
ar
n
tr
ain
i
n
g
d
ata
.
T
h
is
p
r
o
b
lem
is
k
n
o
w
n
b
y
t
h
e
“
E
x
p
lo
d
in
g
s
Gr
ad
ien
ts
”.
T
h
e
s
ec
o
n
d
p
r
o
b
lem
w
it
h
s
i
m
p
le
R
NNs
i
s
th
at
t
h
e
y
d
o
n
o
t
p
r
eser
v
e
th
e
in
f
o
r
m
at
io
n
f
o
r
a
lo
n
g
ti
m
e,
s
o
at
s
o
m
e
p
o
in
t
th
e
n
eu
r
al
n
e
t
w
o
r
k
ca
n
n
o
lo
n
g
er
co
n
n
ec
t
th
e
r
elatio
n
s
h
i
p
s
b
et
w
ee
n
t
h
e
d
ata
an
d
as
a
r
esu
l
t
it
w
o
u
ld
h
a
v
e
d
if
f
ic
u
ltie
s
to
lear
n
lo
n
g
-
ter
m
ad
d
ictio
n
s
T
h
is
p
r
o
b
lem
is
k
n
o
w
n
as
t
h
e
“
Va
n
is
h
i
n
g
g
r
ad
ie
n
t
p
r
o
b
lem
”
.
T
o
o
v
er
co
m
e
e
x
p
lo
d
in
g
/
v
a
n
i
s
h
i
n
g
g
r
ad
ie
n
t
p
r
o
b
lem
s
,
a
n
e
w
co
n
ce
p
t
h
a
s
b
ee
n
in
tr
o
d
u
ce
d
: “
L
ST
M”
ab
b
r
ev
ia
tio
n
o
f
L
o
n
g
S
h
o
r
t
-
T
er
m
Me
m
o
r
y
.
2
.
2
.
3
.
L
ST
M
T
h
is
co
n
ce
p
t
w
as
f
ir
s
t
i
n
tr
o
d
u
ce
d
[
6
]
,
it
is
an
e
x
te
n
s
io
n
o
f
r
ec
u
r
r
en
t
n
e
u
r
al
n
e
t
w
o
r
k
s
to
ex
ten
d
t
h
eir
m
e
m
o
r
y
.
L
ST
Ms
allo
w
R
NNs
to
r
e
m
e
m
b
er
t
h
ei
r
en
tr
ies
o
v
er
a
lo
n
g
p
er
io
d
o
f
ti
m
e,
as
an
L
ST
M
ca
n
w
r
ite
an
d
d
elete
i
n
f
o
r
m
at
io
n
f
r
o
m
i
ts
m
e
m
o
r
y
[
7
]
.
Fig
u
r
e
2
s
h
o
w
s
t
h
is
m
e
m
o
r
y
b
eh
av
es
lik
e
a
b
lo
ck
ed
ce
ll
ie
t
h
e
ce
ll
d
ec
id
es
to
s
t
o
r
e
o
r
d
elete
in
f
o
r
m
atio
n
,
d
ep
en
d
in
g
o
n
t
h
e
i
m
p
o
r
tan
ce
it
attr
ib
u
tes
to
it.
T
h
e
attr
ib
u
tio
n
o
f
i
m
p
o
r
tan
ce
is
d
o
n
e
th
r
o
u
g
h
w
ei
g
h
t
s
,
w
h
ic
h
ar
e
also
lear
n
ed
b
y
t
h
e
al
g
o
r
ith
m
.
I
t
s
i
m
p
l
y
m
ea
n
s
t
h
at
it
lear
n
s
o
v
er
ti
m
e
w
h
a
t
in
f
o
r
m
a
ti
o
n
is
i
m
p
o
r
tan
t
a
n
d
w
h
ich
i
s
n
o
t.
I
t
is
a
g
ate
m
ec
h
a
n
i
s
m
a
n
d
m
e
m
o
r
y
ce
ll.
Fo
r
g
et
Gate
:
T
h
is
b
lo
ck
is
r
es
p
o
n
s
ib
le
f
o
r
r
esetti
n
g
t
h
e
m
e
m
o
r
y
ce
ll
(
s
tate
ce
ll).
T
h
at
is
,
th
e
p
r
ev
io
u
s
l
y
g
iv
e
n
i
n
f
o
r
m
atio
n
i
s
n
o
lo
n
g
er
u
s
e
f
u
l f
o
r
th
e
L
ST
M
to
lear
n
m
o
r
e.
I
n
p
u
t G
ate:
T
h
i
s
b
lo
ck
ta
k
es t
h
e
r
esp
o
n
s
ib
ili
t
y
to
ad
d
th
e
in
f
o
r
m
at
io
n
to
th
e
m
e
m
o
r
y
ce
ll.
Ou
tp
u
t G
ate:
T
h
is
b
lo
ck
is
r
es
p
o
n
s
ib
le
f
o
r
s
elec
ti
n
g
u
s
e
f
u
l i
n
f
o
r
m
atio
n
f
r
o
m
t
h
e
cu
r
r
en
t
m
e
m
o
r
y
ce
ll.
Fig
u
r
e
2
.
L
ST
M
b
lo
ck
[
8
]
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
201
9
:
3
1
7
–
327
320
3.
RE
L
AT
E
D
WO
RK
S
AR
I
M
A
ti
m
e
s
er
ies
ar
e
a
w
i
d
ely
u
s
ed
tech
n
iq
u
e
in
ec
o
n
o
-
m
e
tr
ics
f
o
r
f
i
n
a
n
cial
ti
m
e
s
er
ies
[
9
]
,
s
ev
er
al
AR
I
M
A
m
o
d
el
w
er
e
p
r
o
p
o
s
ed
to
an
al
y
ze
a
n
d
f
o
r
ec
ast
s
t
o
ck
m
ar
k
ets
[
1
0
-
12]
.
Fu
r
th
er
m
o
r
e,
AR
I
M
A
is
u
s
ed
f
o
r
w
ater
b
u
d
g
et
/
co
n
s
u
m
p
tio
n
s
p
r
ed
ictio
n
[
1
3
-
14]
a
n
d
elec
tr
ic
it
y
d
e
m
a
n
d
[
1
5
]
.
Mo
r
e
r
ec
en
tl
y
,
t
h
er
e
h
as
b
ee
n
a
g
r
o
w
in
g
in
ter
e
s
t
i
n
t
h
e
u
s
e
o
f
d
ee
p
lear
n
in
g
m
o
d
els
[
1
6
-
17]
,
esp
ec
iall
y
r
e
c
u
r
r
en
t
m
o
d
els
s
u
c
h
a
s
L
ST
M
Neu
r
al
Net
w
o
r
k
f
o
r
t
h
e
p
r
ed
ictio
n
o
f
f
i
n
an
cia
l
ti
m
e
s
er
ies,
i
n
p
ar
ticu
lar
in
th
e
s
to
ck
m
ar
k
et
[
1
8
-
20]
.
I
n
[
1
8
]
p
r
o
p
o
s
ed
a
m
o
d
elin
g
an
d
p
r
ed
ictio
n
o
f
C
h
i
n
a
s
to
ck
r
etu
r
n
s
u
s
i
n
g
L
ST
M
ar
ch
itect
u
r
e
w
i
th
a
n
ap
p
r
o
v
ed
ac
cu
r
ar
y
o
f
2
7
.
2
%,
i
n
[
1
9
]
an
al
y
ze
d
t
h
e
ap
p
licab
ili
t
y
o
f
r
ec
u
r
r
e
n
t
n
eu
r
al
n
et
w
o
r
k
s
f
o
r
s
to
ck
s
m
ar
k
et
p
r
ices
m
o
v
e
m
en
t
s
p
r
ed
ictio
n
.
Fin
all
y
[
2
0
]
p
r
o
p
o
s
ed
an
ac
cu
r
ate
p
r
ed
ictio
n
o
f
Sh
an
g
h
ai
C
o
m
p
o
s
i
te
I
n
d
ex
an
d
Do
w
J
o
n
es
I
n
d
ex
.
C
o
n
ce
r
n
in
g
th
e
b
u
d
g
et
an
al
y
s
i
s
an
d
f
o
r
ec
asti
n
g
,
v
er
y
lit
tle
w
o
r
k
w
er
e
f
o
u
n
d
co
m
p
ar
i
n
g
o
r
ev
en
ap
p
l
y
in
g
t
h
e
t
w
o
tech
n
iq
u
e
s
,
m
o
s
t
o
f
t
h
e
m
h
as
b
ee
n
ap
p
lied
to
th
e
s
to
ck
p
r
ice
as
p
r
ev
io
u
s
l
y
m
en
tio
n
n
ed
.
T
h
is
is
m
ai
n
l
y
d
u
e
to
th
e
d
if
f
ic
u
lt
y
o
f
o
b
tai
n
in
g
r
elev
an
t d
ata
s
ets,
a
n
d
th
e
v
o
l
atile
n
at
u
r
e
o
f
t
h
ese
d
ata
.
No
n
e
o
f
its
au
t
h
o
r
s
co
m
p
ar
ed
th
e
p
er
f
o
r
m
a
n
ce
o
f
L
ST
M
an
d
AR
I
M
A
m
o
d
els.
4.
F
O
RE
CAS
T
I
N
G
U
SI
N
G
A
RIM
A
RAND
O
M
WAL
K
4
.
1
.
Da
t
a
s
et
s
W
e
u
s
e
a
Data
s
et
th
at
tr
ea
ts
th
e
ac
tu
al
b
u
d
g
et
co
n
s
u
m
ed
b
y
a
g
o
v
er
n
m
e
n
tal
o
r
g
an
izat
io
n
.
T
h
e
d
ata
co
n
tain
ed
i
n
t
h
is
Data
s
et
d
at
es
f
r
o
m
1
9
7
6
to
2
0
1
6
w
it
h
an
an
n
u
al
p
er
io
d
icit
y
Fi
g
u
r
e
3
T
h
e
v
alu
es
i
n
t
h
e
D
ataset
ar
e
ex
p
r
ess
ed
in
b
illi
o
n
d
o
llar
s
.
T
h
e
r
ich
n
ess
an
d
th
e
h
i
s
to
r
y
o
f
th
e
d
ata
allo
w
u
s
to
o
p
tim
ize
th
e
r
elev
an
ce
o
f
o
u
r
an
a
l
y
s
is
.
T
h
e
p
u
r
p
o
s
e
o
f
th
is
an
al
y
s
i
s
is
to
p
r
ed
ict
th
e
b
u
d
g
et
f
o
r
th
e
u
p
c
o
m
in
g
y
ea
r
s
.
Gi
v
e
n
th
at
ti
m
e
s
er
ies
tr
ea
t
a
s
i
n
g
le
ti
m
e
-
d
ep
en
d
en
t
v
ar
iab
le
t
h
at
w
ill
p
r
ed
ict
f
u
tu
r
e
v
a
lu
e
s
b
ased
o
n
p
r
ev
io
u
s
l
y
o
b
s
er
v
ed
v
alu
es.
T
h
e
Data
s
et
r
ec
o
r
d
s
an
d
p
r
o
ce
s
s
es
th
e
an
n
u
al
b
u
d
g
et.
T
h
at
s
aid
,
th
e
“
T
im
es
s
er
ie
s
”
m
o
d
el
is
w
ell
ad
ap
ted
to
th
is
ca
s
e.
I
n
o
r
d
er
to
ap
p
ly
t
h
e
A
R
I
M
A
m
o
d
el,
w
e
f
o
llo
w
t
h
e
B
o
x
-
J
en
k
i
n
s
m
eth
o
d
.
Fig
u
r
e
3
.
Data
d
escr
ip
tio
n
4
.
2
.
P
re
pro
ce
s
s
ing
T
h
is
p
h
ase
is
n
ec
es
s
ar
y
a
s
it
allo
w
s
t
h
e
p
r
ep
ar
atio
n
o
f
d
ata
an
d
m
a
k
e
t
h
e
m
in
ac
co
r
d
an
ce
w
it
h
o
u
r
n
ee
d
s
.
W
e
w
a
n
t
to
tr
ac
k
an
d
p
r
ed
ict
th
e
ev
o
lu
tio
n
o
f
t
h
e
o
v
er
all
b
u
d
g
et
o
f
th
e
o
r
g
a
n
izatio
n
.
T
h
is
Data
s
et
b
r
ea
k
s
d
o
w
n
t
h
e
b
u
d
g
et
b
y
o
f
f
ice
s
an
d
s
er
v
ice
s
f
o
r
ea
ch
y
ea
r
,
s
o
w
e
w
i
ll
co
n
s
o
lid
ate
th
e
b
u
d
g
et
co
n
s
u
m
ed
f
o
r
ea
ch
y
ea
r
o
n
l
y
.
T
o
b
u
ild
an
A
R
I
M
A
(
T
i
m
e
s
er
ies)
m
o
d
el,
it
is
d
e
s
ir
ab
le
to
s
to
r
e
th
e
ti
m
e
(
f
o
r
o
u
r
ca
s
e
y
ea
r
s
)
in
o
n
e
co
l
u
m
n
a
n
d
th
e
v
ar
iab
le
o
n
w
h
ic
h
w
e
w
ill ap
p
l
y
t
h
e
m
o
d
el
i
n
an
o
th
er
co
lu
m
n
.
4
.
3
.
Ana
ly
s
is
I
n
th
is
t
h
ir
d
p
h
a
s
e
o
f
th
e
p
r
o
ce
s
s
,
w
e
a
n
al
y
ze
t
h
e
b
eh
a
v
io
r
o
f
th
e
ti
m
e
s
er
ie
s
,
i
n
o
r
d
er
to
ex
tr
ac
t
t
h
e
u
s
e
f
u
l
in
f
o
r
m
atio
n
u
s
ed
to
b
u
ild
th
e
m
o
d
el
Fig
u
r
e
4
.
W
e
n
o
t
ice
th
r
o
u
g
h
t
h
is
g
r
ap
h
th
at
t
h
e
s
er
ies
is
g
r
o
w
in
g
,
s
o
th
e
b
u
d
g
et
is
g
r
o
w
in
g
o
v
er
ti
m
e.
T
h
er
e
w
a
s
a
d
ec
lin
e
b
et
w
ee
n
t
h
e
y
ea
r
s
2
0
1
0
-
2
0
1
5
th
at
in
ter
s
ec
ts
w
it
h
t
h
e
p
er
io
d
o
f
th
e
ec
o
n
o
m
ic
cr
is
i
s
.
T
h
e
av
er
ag
e
o
f
th
e
s
er
ie
s
te
n
d
s
to
ch
a
n
g
e.
T
h
e
g
r
ap
h
s
h
o
w
s
th
at
t
h
e
s
er
ies
is
n
o
t
s
tatio
n
ar
y
,
to
e
n
s
u
r
e
th
e
s
tatio
n
ar
it
y
o
f
t
h
e
s
er
ies,
Fig
u
r
e
5
we
r
ef
er
to
th
e
test
“
Au
g
m
e
n
ted
Dic
k
e
y
-
F
u
ller
te
s
t”.
T
h
is
test
is
b
ased
o
n
t
w
o
a
s
s
u
m
p
tio
n
s
:
T
h
e
n
u
ll
h
y
p
o
th
e
s
is
: th
e
s
er
ie
s
ca
n
b
e
r
ep
r
esen
ted
b
y
a
u
n
it r
o
o
t,
s
o
it is
n
o
t statio
n
ar
y
.
T
h
e
alter
n
ativ
e
h
y
p
o
t
h
esi
s
:
r
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Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
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8938
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
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8
,
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4
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Dec
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er
201
9
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1
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–
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8
2
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
F
o
r
ec
a
s
tin
g
fin
a
n
cia
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b
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time
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A
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d
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vs LS
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... (
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R
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323
Fig
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Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
2
2
5
2
-
8938
IJ
-
A
I
Vo
l.
8
,
No
.
4
,
Dec
em
b
er
201
9
:
3
1
7
–
327
324
Fig
u
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10
.
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o
r
th
e
n
ex
t
y
ea
r
s
Fo
r
ec
asts
a
n
d
t
h
e
as
s
o
ciate
d
c
o
n
f
id
e
n
ce
i
n
ter
v
al
t
h
at
w
e
g
e
n
er
ated
ar
e
u
s
ed
to
b
etter
u
n
d
er
s
tan
d
t
i
m
e
s
er
ies
an
d
p
r
ed
ict
w
h
at
to
ex
p
ec
t.
Fo
r
ec
asts
s
h
o
w
t
h
at
t
h
e
b
u
d
g
et
s
h
o
u
ld
co
n
tin
u
e
to
g
r
o
w
at
a
s
tead
y
p
ac
e.
As
lo
n
g
as
w
e
ar
e
p
lan
n
i
n
g
th
e
b
u
d
g
et
f
o
r
y
ea
r
s
to
co
m
e,
it
is
n
at
u
r
al
f
o
r
u
s
to
b
ec
o
m
e
le
s
s
co
n
f
id
en
t
in
o
u
r
v
alu
e
s
.
T
h
is
is
r
e
f
lecte
d
i
n
t
h
e
co
n
f
id
en
ce
i
n
ter
v
als
g
e
n
er
ate
d
b
y
o
u
r
m
o
d
el,
w
h
ic
h
g
r
o
w
a
s
w
e
m
o
v
e
f
u
r
t
h
er
in
to
th
e
f
u
tu
r
e.
5.
F
O
RE
CAS
T
I
N
G
U
SI
N
G
L
S
T
M
I
n
t
h
is
s
ec
tio
n
w
e
w
a
n
t
to
p
r
ed
ict
th
e
b
u
d
g
et
f
o
r
y
ea
r
s
to
co
m
e
u
s
i
n
g
Dee
p
L
ea
r
n
in
g
v
ia
t
h
e
L
ST
M
ar
ch
itect
u
r
e.
No
te
th
at
w
e
p
r
ev
io
u
s
l
y
p
r
ed
icted
th
e
b
u
d
g
e
t
u
s
in
g
t
h
e
A
R
I
M
A
m
o
d
el.
W
e
u
s
e
T
en
s
er
f
lo
w
a
n
d
Ker
as
lib
r
ar
ies
to
im
p
le
m
en
t
t
h
is
ar
ch
i
tectu
r
e.
B
u
d
g
et
d
ata
is
s
av
ed
as
s
eq
u
e
n
ce
s
.
T
o
m
an
ag
e
th
e
d
ep
en
d
en
c
e
o
f
th
e
s
eq
u
e
n
ce
s
w
e
u
s
e
th
e
r
ec
u
r
r
en
t
n
e
u
r
al
n
et
w
o
r
k
s
,
p
r
ec
is
el
y
a
n
L
ST
M
s
in
ce
it
p
r
eser
v
es
t
h
e
in
f
o
r
m
atio
n
f
o
r
a
lo
n
g
d
u
r
atio
n
an
d
allo
w
s
to
m
o
d
el
th
e
m
o
s
t
s
o
p
h
is
tic
ated
d
ep
en
d
en
cies
in
o
u
r
ti
m
e
s
er
ies.
T
h
is
m
o
d
el
s
u
p
p
o
r
ts
a
v
er
y
lar
g
e
v
o
lu
m
e
o
f
d
ata.
An
L
ST
M
h
as
t
h
r
ee
p
ar
a
m
eter
s
:
o
n
e
p
ar
a
m
eter
to
w
r
ite
th
e
i
n
f
o
r
m
atio
n
in
th
e
m
e
m
o
r
y
,
t
h
e
o
th
er
to
r
ea
d
it a
n
d
th
e
last
o
n
e
to
d
elete
it.
I
n
th
i
s
p
h
ase
w
e
d
is
c
u
s
s
t
h
e
ar
ch
itect
u
r
e
o
f
th
e
p
r
o
p
o
s
ed
L
S
T
M
m
o
d
el:
T
h
e
s
ec
o
n
d
s
tep
is
to
s
tan
d
a
r
d
ize
th
e
d
ata,
ie
th
e
d
ata
m
u
s
t
b
elo
n
g
to
th
e
s
co
p
e
o
f
th
e
ac
ti
v
atio
n
f
u
n
ctio
n
.
C
h
o
ice
o
f
th
e
ac
ti
v
atio
n
f
u
n
c
tio
n
.
Fo
r
t
h
i
s
s
tu
d
y
w
e
o
p
ted
f
o
r
a
s
i
g
m
o
id
f
u
n
ctio
n
t
h
at
o
u
tp
u
ts
v
a
lu
e
s
b
et
w
ee
n
0
an
d
1
.
W
e
u
s
e
th
e
h
y
p
er
b
o
lic
tan
g
e
n
t f
u
n
ctio
n
.
“
B
atch
s
ize”
is
t
h
e
n
u
m
b
er
o
f
s
a
m
p
les t
h
at
w
i
ll b
e
p
r
o
p
ag
ated
in
th
e
n
e
u
r
al
n
et
w
o
r
k
.
T
h
e
n
eu
r
al
n
et
w
o
r
k
r
eq
u
ir
es o
n
l
y
o
n
e
o
u
tp
u
t to
es
ti
m
ate
th
e
b
u
d
g
et
f
o
r
th
e
n
e
x
t
y
ea
r
.
Af
ter
b
u
i
ld
in
g
t
h
e
m
o
d
e
l,
it
is
i
m
p
o
r
tan
t to
t
h
o
r
o
u
g
h
l
y
e
v
al
u
ate
th
e
m
o
d
el.
T
o
d
o
th
is
,
w
e
u
s
e
t
h
e
R
MSE
co
s
t f
u
n
ctio
n
.
T
h
is
f
u
n
ctio
n
ca
lcu
late
s
th
e
er
r
o
r
b
et
w
ee
n
t
h
e
p
r
ed
icted
d
ata
an
d
th
e
test
d
ata.
5
.
1
.
M
o
del
co
ns
t
ruct
io
n
I
n
t
h
is
s
tep
w
e
b
u
ild
a
n
ap
p
r
o
p
r
iate
L
ST
M
m
o
d
el
f
o
r
o
u
r
ca
s
e
s
t
u
d
y
.
A
n
L
ST
M
m
o
d
el
as
s
u
m
e
s
t
h
a
t
o
u
r
d
ata
is
d
i
v
id
ed
in
to
i
n
p
u
t
X
an
d
o
u
tp
u
t
Y
co
m
p
o
n
e
n
ts
.
Fo
r
o
u
r
ca
s
e,
w
e
u
s
e
t
h
e
p
r
ev
i
o
u
s
o
b
s
er
v
atio
n
s
f
o
r
ea
ch
ti
m
e
s
tep
as
o
u
r
in
p
u
t
s
an
d
th
e
o
u
tp
u
t
w
i
ll
b
e
th
e
o
b
s
er
v
atio
n
o
f
th
e
cu
r
r
e
n
t
ti
m
e
s
tep
.
T
h
e
f
o
llo
w
in
g
F
ig
u
r
e
12
r
ep
r
esen
ts
th
e
o
v
er
a
ll c
o
n
f
i
g
u
r
atio
n
o
f
o
u
r
L
ST
M.
Fig
u
r
e
12
.
Glo
b
al
d
iag
r
am
o
f
t
h
e
L
ST
M
Evaluation Warning : The document was created with Spire.PDF for Python.
IJ
-
AI
I
SS
N:
2252
-
8938
F
o
r
ec
a
s
tin
g
fin
a
n
cia
l
b
u
d
g
et
time
s
erie
s
:
A
R
I
MA
r
a
n
d
o
m
w
a
lk
vs LS
TM
n
eu
r
a
l
... (
Ma
r
ye
m
R
h
a
n
o
u
i
)
325
T
o
b
u
ild
an
L
ST
M
m
o
d
el
w
e
m
u
s
t
f
ir
s
t
tr
an
s
f
o
r
m
th
e
tr
ain
in
g
an
d
tes
t
Data
s
et
i
n
to
a
th
r
ee
-
d
i
m
en
s
io
n
al
ar
r
a
y
o
f
“
s
a
m
p
le
s
,
f
ea
t
u
r
es
an
d
t
i
m
e
s
tep
s
”.
W
e
u
s
e
an
i
n
p
u
t
la
y
er
,
a
h
id
d
en
la
y
er
co
n
tai
n
i
n
g
L
ST
M
b
lo
ck
s
a
n
d
a
s
i
n
g
le
o
u
tp
u
t
la
y
er
.
W
e
m
ad
e
u
s
e
o
f
th
e
d
e
f
a
u
lt
ac
t
iv
at
io
n
f
u
n
ctio
n
o
f
an
L
ST
M:
s
ig
m
o
id
.
T
h
e
m
o
d
el
is
tr
ain
ed
1
0
0
0
tim
es
w
i
th
b
at
ch
s
ize
eq
u
al
s
to
1
0
.
W
e
u
s
e
A
DM
o
p
ti
m
izatio
n
alg
o
r
ith
m
f
o
r
u
p
d
atin
g
w
e
ig
h
ts
.
W
e
u
s
ed
t
h
e
f
o
llo
w
i
n
g
r
u
les
to
d
eter
m
i
n
e
t
h
e
n
u
m
b
er
o
f
la
y
er
s
a
n
d
th
e
n
u
m
b
er
o
f
n
e
u
r
o
n
s
in
ea
c
h
la
y
er
:
I
n
p
u
t
la
y
er
:
lo
g
icall
y
w
e
h
av
e
o
n
e
e
n
tr
y
,
th
e
n
u
m
b
er
o
f
n
e
u
r
o
n
s
co
n
tain
ed
in
t
h
is
la
y
er
is
d
eter
m
i
n
ed
b
y
th
e
n
u
m
b
er
o
f
q
u
an
ti
f
iab
le
co
l
u
m
n
s
.
Fo
r
o
u
r
ca
s
e
w
e
w
an
t
t
o
f
o
llo
w
th
e
e
v
o
l
u
tio
n
o
f
t
h
e
b
u
d
g
et,
s
o
t
h
e
n
u
m
b
er
o
f
n
e
u
r
o
n
s
in
t
h
e
in
p
u
t la
y
er
is
1
.
Ou
tp
u
t
la
y
er
:
ea
ch
n
e
u
r
al
n
et
w
o
r
k
h
a
s
a
s
in
g
le
o
u
tp
u
t.
Si
n
ce
w
e
w
a
n
t
to
co
n
tr
o
l
th
e
b
u
d
g
et,
o
u
r
o
u
tp
u
t
la
y
er
co
n
tai
n
s
o
n
l
y
o
n
e
n
eu
r
o
n
.
Hid
d
e
n
la
y
er
: t
h
e
s
ize
o
f
t
h
is
l
a
y
er
,
th
at
is
to
s
a
y
t
h
e
n
u
m
b
er
o
f
n
e
u
r
o
n
s
,
is
to
d
eter
m
i
n
e.
W
e
test
ed
v
ar
io
u
s
L
ST
M
co
n
f
ig
u
r
at
io
n
s
u
s
in
g
d
if
f
er
e
n
t
n
u
m
b
er
s
o
f
b
lo
ck
s
.
T
ab
le
2
s
h
o
w
s
co
m
p
ar
e
s
th
e
d
if
f
er
e
n
t
co
n
f
i
g
u
r
atio
n
s
b
ased
o
n
th
e
R
MSE
.
I
t
r
ev
ea
l
s
th
at
i
n
t
h
e
b
est
co
n
f
i
g
u
r
atio
n
is
t
h
e
o
n
e
w
it
h
2
L
ST
M
b
lo
ck
s
.
Fig
u
r
e
1
3
d
escr
ib
es
th
e
ad
o
p
ted
L
ST
M
ar
ch
itectu
r
e,
it
illu
s
tr
ates
th
e
f
lo
w
o
f
an
X
ti
m
e
s
er
ies
th
r
o
u
g
h
an
L
ST
M
la
y
er
.
No
te
th
at
Y
r
ep
r
esen
t
s
t
h
e
o
u
tp
u
t
a
n
d
c
r
ep
r
esen
ts
th
e
m
e
m
o
r
y
.
T
h
e
f
ir
s
t
L
ST
M
u
n
it
tak
es
t
h
e
in
itia
l
s
tate
o
f
th
e
n
et
w
o
r
k
a
n
d
th
e
f
ir
s
t
-
t
i
m
e
s
tep
o
f
th
e
s
eq
u
en
ce
X1
an
d
th
e
n
ca
lcu
lates
th
e
f
ir
s
t
o
u
tp
u
t
Y1
an
d
th
e
m
e
m
o
r
y
c1
.
A
t
ti
m
e
t,
th
e
u
n
i
t
tak
e
s
th
e
cu
r
r
en
t
s
tate
o
f
th
e
n
et
w
o
r
k
(
ct−
1
,
Yt−1
)
an
d
th
e
n
ex
t
ti
m
e
s
tep
o
f
t
h
e
s
eq
u
en
ce
Xt,
th
e
n
ca
lcu
lates
t
h
e
o
u
tp
u
t
Xt
an
d
th
e
m
e
m
o
r
y
ct.
E
ac
h
L
ST
M
u
n
it
b
eh
a
v
e
s
lik
e
a
m
i
n
i
-
m
e
m
o
r
y
w
h
er
e
th
e
f
o
r
g
et
g
ate,
in
p
u
t
g
ate
an
d
o
u
tp
u
t
g
ate
h
a
v
e
w
eig
h
t
s
th
at
ar
e
lear
n
ed
d
u
r
in
g
th
e
tr
ain
i
n
g
p
r
o
ce
d
u
r
e.
T
ab
le
2
.
L
ST
M
co
n
f
ig
u
r
atio
n
s
M
o
d
e
l
R
M
S
E
M
S
E
M
A
E
1
B
l
o
c
k
L
S
T
M
0
.
2
2
6
0
.
0
5
1
0
.
1
2
0
2
B
l
o
c
k
L
S
T
M
0
.
2
2
2
0
.
0
4
9
0
.
1
1
9
3
B
l
o
c
k
L
S
T
M
0
.
2
8
1
0
.
0
7
9
0
.
1
7
8
4
B
l
o
c
k
L
S
T
M
0
.
2
2
9
0
.
0
5
2
0
.
1
2
2
5
B
l
o
c
k
L
S
T
M
0
.
2
8
4
0
.
0
8
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Fig
u
r
e
13
.
L
ST
M
A
r
ch
itec
tu
r
e
6.
M
O
DE
L
S S
YNTH
E
S
I
S AN
D
CO
M
P
ARAISON
I
n
o
r
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er
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th
e
e
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o
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tio
n
o
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h
e
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u
d
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et
w
e
f
o
llo
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ed
t
w
o
m
e
th
o
d
s
:
AR
I
M
A
an
d
L
ST
M.
I
n
t
h
is
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tio
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e
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al
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at
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e
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els
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ar
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ig
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itect
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ased
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o
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ar
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ased
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M
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t
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t
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Dat
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T
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A
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8
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4
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Dec
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b
er
201
9
:
3
1
7
–
327
326
ca
lcu
latio
n
allo
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s
u
s
to
ev
al
u
ate
th
e
ac
cu
r
ac
y
o
f
a
m
o
d
el.
T
h
e
T
ab
le
5
s
h
o
w
s
t
h
e
L
ST
M
m
o
d
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i
s
o
n
ce
ag
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i
n
b
etter
th
an
t
h
e
A
R
I
M
A
m
o
d
el.
Fig
u
r
e
14
.
Vis
u
aliza
tio
n
o
f
t
h
e
p
r
ed
ictio
n
s
o
f
th
e
t
w
o
m
o
d
els
T
ab
le
3.
R
MSE
co
m
p
ar
aiso
n
M
o
d
e
l
R
M
S
E
M
a
c
h
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L
e
a
r
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n
g
:
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R
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0
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2
3
9
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e
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n
i
n
g
:
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S
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M
0
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2
2
2
T
ab
le
4
.
MA
E
co
m
p
ar
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M
o
d
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l
M
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E
M
a
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h
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L
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r
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1
3
9
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1
1
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.
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m
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ar
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o
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l
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a
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9
6
.
1
.
M
a
j
o
r
diff
er
ence
s
bet
wee
n AR
I
M
A
a
nd
L
ST
M
A
lt
h
o
u
g
h
t
h
e
r
esear
c
h
i
s
r
ec
en
t,
it is
clea
r
t
h
at
L
ST
M
ar
ch
ite
ctu
r
es
h
a
v
e
g
r
ea
t p
o
ten
tial
as
ca
n
d
id
ate
s
f
o
r
ti
m
e
s
er
ies
m
o
d
eli
n
g
a
n
d
f
o
r
ec
asti
n
g
.
W
e
s
t
u
d
y
i
n
t
h
e
f
o
llo
w
i
n
g
T
ab
le
6
th
e
m
aj
o
r
d
if
f
er
en
ce
s
b
et
w
ee
n
a
n
L
ST
M
an
d
AR
I
M
A
.
T
h
e
u
s
e
o
f
R
N
Ns
i
n
cl
u
d
in
g
t
h
e
L
ST
M
ar
ch
itectu
r
e,
allo
w
s
th
e
s
etti
n
g
o
f
s
ev
er
al
p
ar
am
eter
s
th
at
w
e
m
u
s
t
ad
j
u
s
t
to
o
b
tain
o
p
ti
m
al
p
er
f
o
r
m
a
n
ce
o
n
t
h
e
f
o
r
ec
ast
in
g
tas
k
s
.
I
ts
d
if
f
icu
lt
y
lies
i
n
ch
o
o
s
in
g
t
h
e
r
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g
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t
p
ar
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m
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ter
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to
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n
d
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h
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t
m
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el
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ch
it
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tu
r
e.
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AR
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M
A
m
o
d
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is
s
i
m
p
le
to
co
n
f
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g
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r
e
as
it
g
i
v
es
a
g
o
o
d
p
er
f
o
r
m
a
n
c
e,
th
is
m
o
d
e
l
al
s
o
r
eq
u
ir
es
th
e
id
en
tific
atio
n
o
f
th
e
p
ar
a
m
et
er
s
p
,
d
an
d
q
s
u
ch
th
at
p
i
s
t
h
e
o
r
d
er
o
f
th
e
a
u
t
o
r
eg
r
ess
i
v
e
p
ar
t
(
AR
)
,
o
f
th
e
o
r
d
er
o
f
d
if
f
er
e
n
tiatio
n
an
d
q
th
e
o
r
d
er
o
f
th
e
m
o
v
i
n
g
av
er
a
g
e
p
ar
t (
MA
)
.
T
ab
le
6
.
Mo
d
els co
m
p
ar
aiso
n
A
R
I
M
A
L
S
T
M
L
i
n
e
a
r
mo
d
e
l
N
o
n
l
i
n
e
a
r
mo
d
e
l
S
mal
l
a
mo
u
n
t
o
f
d
a
t
a
L
a
r
g
e
a
mo
u
n
t
o
f
d
a
t
a
P
a
r
a
me
t
r
i
c
mo
d
e
l
,
t
h
a
t
i
s
t
o
s
a
y
f
o
r
e
a
c
h
se
r
i
e
s w
e
h
a
v
e
t
o
d
e
f
i
n
e
t
h
e
p
a
r
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me
t
e
r
s p
,
d
a
n
d
q
N
o
n
-
p
a
r
a
me
t
r
i
c
mo
d
e
l
,
r
e
q
u
i
r
e
s a
d
j
u
s
t
me
n
t
o
f
so
me
h
y
p
e
r
me
t
e
r
s
D
e
d
i
c
a
t
e
d
s
p
e
c
i
f
i
c
a
l
l
y
f
o
r
t
i
me
se
r
i
e
s
P
r
o
c
e
ss se
q
u
e
n
t
i
a
l
d
a
t
a
7.
CO
NCLU
SI
O
N
Def
i
n
i
n
g
a
n
o
p
ti
m
al
m
o
d
el
to
f
o
r
ec
ast
f
i
n
a
n
cial
ti
m
e
s
er
ie
s
d
ata
is
a
ch
alle
n
g
i
n
g
tas
k
b
ec
au
s
e
o
f
t
h
e
n
o
n
-
li
n
ea
r
it
y
,
n
o
n
-
s
tatio
n
ar
it
y
an
d
v
o
latili
t
y
c
h
ar
ac
ter
is
t
ic
s
o
f
t
h
i
s
t
y
p
e
o
f
d
ata.
I
n
t
h
i
s
p
ap
er
w
e
co
m
p
ar
ed
t
w
o
f
o
r
ec
asti
n
g
m
o
d
els
f
o
r
f
i
n
an
cia
l
ti
m
e
s
er
ies.
T
h
is
p
r
ed
ictiv
e
an
al
y
s
is
s
h
o
w
ed
th
a
t,
alth
o
u
g
h
t
h
e
AR
I
M
A
m
o
d
el
p
r
o
v
id
es
s
ati
s
f
ac
to
r
y
r
esu
lt
s
,
t
h
e
L
ST
M
m
o
d
el
o
u
tp
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