I
n
t
e
r
n
at
ion
al
Jou
r
n
al
of
E
lec
t
r
ical
an
d
Com
p
u
t
e
r
E
n
gin
e
e
r
in
g
(
I
JE
CE
)
Vol.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
,
pp.
614
~
623
I
S
S
N:
2088
-
8708
,
DO
I
:
10
.
11591/i
jec
e
.
v
15
i
1
.
pp
6
14
-
623
614
Jou
r
n
al
h
omepage
:
ht
tp:
//
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s
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ti
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hor
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memor
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or
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a
s
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ne
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a
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gr
e
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ter
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ti
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s
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n
d
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t
h
e
CC
B
Y
-
SA
l
i
ce
n
s
e.
C
or
r
e
s
pon
din
g
A
u
th
or
:
Nr
us
ingha
T
r
ipathy
De
pa
r
tm
e
nt
of
C
omput
e
r
S
c
ienc
e
a
nd
E
nginee
r
ing
,
S
iks
ha
‘
O
’
Anus
a
ndha
n
(
De
e
med
to
be
Unive
r
s
it
y
)
B
huba
ne
s
wa
r
,
751030,
I
ndia
E
mail:
n
r
us
inghatr
ipathy654@gmail.
c
om
1.
I
NT
RODU
C
T
I
ON
S
ince
2009,
whe
n
B
it
c
oin
wa
s
f
ir
s
t
pr
opos
e
d
by
S
a
tos
hi
Na
ka
mot
o,
the
dig
it
a
l
c
u
r
r
e
nc
y
mar
ke
t
ha
s
a
tt
r
a
c
ted
a
lot
of
a
tt
e
nti
on.
S
ince
Apr
i
l
2019
[
1]
,
B
it
c
oin
ha
s
gr
own
to
be
the
mos
t
p
r
of
it
a
ble
a
nd
we
l
l
-
known
c
r
yptocur
r
e
nc
y
wor
ldwide.
B
e
c
a
us
e
bus
ines
s
e
s
t
ha
t
a
r
e
li
s
ted
on
s
tock
mar
ke
ts
a
lr
e
a
dy
pos
s
e
s
s
B
it
c
oin,
s
e
ve
r
a
l
f
inanc
ial
ins
ti
tut
ions
ha
ve
s
tar
ted
to
inves
t
in
the
d
igi
tal
a
s
s
e
t's
wor
th.
B
ut
a
s
a
f
inanc
ial
tool
,
B
it
c
oin
is
a
ls
o
r
e
nowne
d
f
or
it
s
e
xtr
e
me
volatil
it
y
[
2]
.
Nume
r
ous
f
a
c
tor
s
,
s
uc
h
a
s
tr
a
ns
a
c
ti
on
volum
e
a
nd
f
r
e
que
nc
y,
a
f
f
e
c
t
thi
s
volatil
it
y.
T
he
s
e
notable
va
r
iations
ne
e
d
to
be
take
n
int
o
a
c
c
ount
by
inves
tor
s
whe
n
c
hoos
ing
their
inves
tm
e
nts
.
S
tudi
e
s
ha
ve
indi
c
a
ted
that
the
volatil
it
y
of
B
it
c
oin
de
mons
tr
a
tes
a
pr
o
-
c
yc
li
c
a
l
tende
nc
y,
incr
e
a
s
ing
in
tande
m
with
he
ight
e
ne
d
global
e
c
onomi
c
a
c
ti
vit
y.
T
he
volatil
it
y
of
B
it
c
oin
r
e
a
c
ts
dif
f
e
r
e
ntl
y
to
incr
e
a
s
e
d
volatil
it
y
in
the
US
s
tock
mar
ke
t
than
do
e
s
the
gold
mar
ke
t
[
3]
,
[
4
]
.
P
r
e
vious
s
tudi
e
s
ha
ve
modele
d
the
volatil
it
y
s
ubtl
e
ti
e
s
o
f
digi
tal
c
ur
r
e
nc
ies
a
nd
f
ound
that
out
-
of
-
s
a
mpl
e
va
lue
a
t
r
is
k
(
Va
R
)
f
o
r
e
c
a
s
ti
ng
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
B
it
c
oin
v
olat
il
it
y
for
e
c
as
ti
ng:
a
c
ompar
ati
v
e
analys
is
of
c
onv
e
nti
onal
…
(
N
r
us
ingha
T
r
ipat
hy
)
615
tec
hniques
f
or
c
r
yptocur
r
e
nc
ies
de
viate
f
r
om
o
pti
mal
in
-
s
a
mpl
e
ge
ne
r
a
li
z
e
d
a
utor
e
gr
e
s
s
ive
c
ondit
ional
he
ter
os
ke
da
s
ti
c
it
y
(
GA
R
C
H)
-
typ
e
pa
r
a
mete
r
s
[
5]
.
T
his
pa
pe
r
a
ddr
e
s
s
e
s
the
pr
oblem
of
a
c
c
ur
a
tely
f
or
e
c
a
s
ti
ng
B
it
c
oin's
volatil
it
y,
a
c
r
uc
ial
tas
k
f
o
r
inves
tor
s
a
nd
f
inanc
ial
a
na
lys
ts
given
B
it
c
oin's
s
ig
nif
ica
nt
pr
ice
f
luctua
ti
ons
.
T
he
p
r
opos
e
d
s
olut
ion
i
nvolves
a
c
ompar
a
ti
ve
a
na
lys
is
of
c
onve
nti
ona
l
e
c
ono
metr
ic
models
a
nd
a
dva
nc
e
d
de
e
p
le
a
r
ning
a
lgor
it
hms
.
S
pe
c
if
ica
ll
y,
f
or
volatil
it
y
f
or
e
c
a
s
ti
ng
we
us
e
hi
ghly
c
ompl
e
x
mul
t
ivar
iate
b
idi
r
e
c
ti
ona
l
long
s
hor
t
-
ter
m
memor
y
(
B
i
-
L
S
T
M
)
ne
twor
ks
.
Bi
-
L
S
T
M
ne
twor
ks
de
mons
tr
a
ted
ve
r
y
high
ve
r
s
a
ti
li
ty
in
dif
f
e
r
e
nt
pr
e
diction
tas
ks
,
whic
h
is
e
videnc
e
f
or
their
s
uit
a
bil
it
y
in
the
c
ons
tantly
e
volvi
ng
B
it
c
oin
mar
ke
t
[
6]
,
[
7]
.
F
r
om
the
r
e
s
ult
s
a
c
hieve
d
in
th
is
s
tudy
it
c
a
n
b
e
c
onc
luded
that
modelli
ng
with
the
mul
ti
va
r
iate
Bi
-
L
S
T
M
model
s
is
mor
e
e
f
f
e
c
ti
ve
than
the
c
las
s
ica
l
e
c
onometr
ic
pr
oc
e
dur
e
s
in
B
it
c
oin
volatil
it
y
f
or
e
c
a
s
ti
ng.
T
he
de
e
p
lea
r
ning
models
a
c
hieve
mor
e
a
c
c
ur
a
te
a
nd
r
obus
t
of
volatil
i
ty
f
o
r
e
c
a
s
ts
s
ince
the
models
the
int
e
r
de
pe
nde
nc
e
of
the
input
va
r
iable
s
invol
ve
d.
T
he
c
ontr
ibut
ion
of
thi
s
wor
k
is
to
e
xtend
the
e
xis
ti
ng
knowle
dge
a
bout
the
na
tu
r
e
of
B
it
c
oin
’
s
volatil
it
y
a
nd
to
o
f
f
e
r
r
e
s
pons
e
s
to
p
r
a
c
ti
ti
o
ne
r
s
a
nd
inves
tor
s
de
a
li
ng
with
unc
e
r
tainty
a
t
tac
he
d
to
the
p
r
oc
e
s
s
of
ope
r
a
ti
ng
on
c
r
yptocur
r
e
nc
y
mar
ke
ts
.
T
he
r
e
s
t
of
the
manus
c
r
ipt
is
or
ga
nize
d
a
s
f
oll
ows
:
S
e
c
ti
on
2
de
s
c
r
ibes
the
mate
r
ials
a
nd
methodologi
e
s
.
S
e
c
ti
on
3
c
ove
r
s
the
model
de
s
c
r
i
pti
ons
.
S
e
c
ti
on
4
pr
e
s
e
nts
the
r
e
s
ult
a
na
lys
is
,
f
oll
owe
d
by
the
c
onc
lus
ion
a
nd
f
utur
e
s
c
ope
of
thi
s
wo
r
k
in
s
e
c
ti
on
5.
2.
M
AT
E
R
I
AL
S
AN
D
M
E
T
HO
DS
B
it
c
oin
da
il
y
r
e
tu
r
n
r
e
f
e
r
s
to
the
va
r
iation
in
B
it
c
oin's
pr
ice
f
r
om
the
e
nd
of
one
da
y
to
the
ne
xt,
e
xpr
e
s
s
e
d
a
s
it
s
na
tur
a
l
logar
it
hm.
C
a
lcula
ti
ng
B
it
c
oin's
r
e
a
li
z
e
d
volatil
it
y
invol
ve
s
a
na
lyzing
it
s
da
il
y
ope
ning,
high
,
low,
a
nd
c
los
ing
pr
ice
s
.
T
he
B
T
C
-
USD
e
xc
ha
nge
r
a
te
da
tas
e
t
us
e
d
in
thi
s
s
tudy
is
s
our
c
e
d
f
r
om
the
wide
ly
us
e
d
P
ython
li
br
a
r
y
Ya
hoo
F
inanc
e
API
,
s
pa
nning
f
r
om
Oc
tober
2014
to
F
e
b
r
ua
r
y
2
022.
T
he
da
tas
e
t
include
s
ti
mes
tamps
,
ope
ning,
high
,
low,
a
nd
c
los
ing
pr
ice
s
,
a
s
we
ll
a
s
volum
e
_(
B
T
C
)
,
r
e
t
ur
ns
,
a
nd
log_r
e
tur
ns
.
T
he
dis
tr
ibut
ion
plot
s
o
f
the
da
tas
e
t's
r
e
tur
ns
a
nd
log
r
e
tur
ns
a
r
e
s
hown
in
F
igu
r
e
1.
F
igur
e
1.
Dis
tr
ibut
ion
plot
s
of
r
e
tu
r
ns
a
nd
log
r
e
tur
ns
T
he
pr
icing
of
B
it
c
oin
is
highl
y
s
e
ns
it
ive
to
s
pe
c
ulative
tr
a
ding
mos
tl
y
in
the
s
hor
t
-
ter
m
a
s
tr
a
de
r
s
us
e
pr
ice
s
wings
to
ga
in
quick
income
.
C
hoice
of
models
a
nd
unde
r
s
tanding
the
da
ta
s
tr
uc
tur
e
r
e
quir
e
s
e
xa
mi
na
ti
on
of
the
a
utocor
r
e
lation
f
unc
ti
on
(
AC
F
)
a
nd
pa
r
ti
a
l
a
utocor
r
e
lation
f
unc
ti
on
(
P
AC
F
)
o
f
B
it
c
oin
pr
ice
da
ta
[
8]
.
P
a
r
t
icula
r
ly,
the
AC
F
de
ter
mi
ne
s
th
e
leve
l
of
r
e
lation
be
twe
e
n
the
ti
me
s
e
r
ies
a
nd
the
l
a
gge
d
or
the
pr
e
vious
va
lues
of
the
va
r
iable
a
t
dis
ti
nc
t
i
nter
va
ls
to
de
ter
mi
ne
whe
ther
the
da
ta
obe
ys
th
e
r
ule
of
s
e
r
iation
de
pe
nde
nc
e
.
I
n
thi
s
c
a
s
e
,
it
be
c
omes
pos
s
ibl
e
to
de
ter
mi
ne
the
de
gr
e
e
o
f
a
utocor
r
e
lation
in
t
he
pr
ice
s
of
B
it
c
oin
a
nd
thi
s
wi
ll
e
na
ble
one
to
pr
e
dict
f
utur
e
pr
ice
moveme
nts
.
J
us
t
li
ke
the
P
AC
F
,
it
he
lps
in
identif
ying
how
c
los
e
ly
a
ti
me
s
e
r
ies
a
nd
lag
va
lues
a
r
e
r
e
late
d
a
nd
he
nc
e
i
t
he
lps
in
identi
f
ying
the
a
ppr
opr
iate
lag
or
de
r
o
f
t
im
e
s
e
r
ies
models
[
9
]
.
T
his
a
na
lys
is
is
mainly
im
por
tant
in
the
pr
oc
e
s
s
of
s
a
ti
s
f
a
c
tor
y
modeling
of
B
T
C
-
USD
da
ta.
Ar
it
h
m
e
ti
c
r
e
tur
ns
a
nd
logar
it
hmi
c
r
e
tu
r
ns
s
tanda
r
dize
t
he
pr
ice
c
ha
nge
s
,
thi
s
make
s
us
e
of
r
e
tur
ns
to
a
na
lyze
a
s
s
e
ts
f
lexible
a
nd
uni
f
or
m
a
t
dif
f
e
r
e
nt
ti
me
hor
izon
s
.
S
ince
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
614
-
623
616
thes
e
a
r
e
nomi
na
l
va
lues
that
e
xc
lude
the
a
c
tual
pr
ice
s
c
a
le,
they
e
xpr
e
s
s
a
s
pe
r
c
e
ntage
va
r
iations
in
pr
ice
;
he
nc
e
,
they
c
a
n
be
us
e
f
ul
in
de
ter
mi
ning
the
va
r
iat
ion
e
xtents
in
the
pr
ice
ove
r
ti
me
[
10]
,
[
11]
.
Nor
m
a
li
z
a
ti
on
or
s
c
a
li
ng
is
im
por
tant
a
s
it
e
ns
ur
e
s
that
a
ll
the
e
xtr
a
c
ted
f
e
a
tur
e
s
c
ontr
ibut
e
e
qua
ll
y
to
the
lea
r
ning
pr
oc
e
s
s
of
the
model,
r
a
ther
than
one
c
ha
r
a
c
ter
is
ti
c
ove
r
powe
r
ing
thos
e
f
or
e
qua
l
s
igni
f
ica
nc
e
.
M
e
thods
li
ke
im
putation
or
de
letion
of
the
mi
s
s
ing
va
lues
he
lp
in
man
a
ging
thes
e
ga
ps
while
in
the
pr
e
pr
oc
e
s
s
ing
s
t
e
p.
Da
ta
pr
e
pr
oc
e
s
s
ing
is
c
r
uc
ial
in
B
it
c
oin
p
r
e
diction
a
s
it
make
s
da
ta
f
it
to
be
us
e
d
in
modeling
a
nd
a
na
lys
is
.
T
h
is
in
tur
n
im
p
r
ove
s
the
a
lr
e
a
dy
p
r
oduc
e
d
f
or
e
c
a
s
ts
a
nd
i
nc
r
e
a
s
e
s
their
leve
l
of
r
e
li
a
bil
it
y
[
12]
.
3.
M
ODE
L
B
UI
L
DI
NG
T
he
a
na
lys
is
of
the
s
pe
c
if
ied
e
c
onomi
c
indi
c
a
tor
s
a
nd
da
ta
a
na
lys
is
methods
is
mor
e
wide
s
pr
e
a
d
us
e
d
in
the
us
a
ge
of
the
c
r
yptocur
r
e
nc
y
pr
e
dictio
n
models
that
pr
ovides
the
unde
r
s
tanding
o
f
the
s
pe
c
if
ied
mar
ke
t
tr
e
nds
.
T
he
models
o
f
p
r
e
diction
that
ha
ve
be
e
n
we
ll
de
ve
loped
t
r
y
to
c
or
r
e
c
t
in
f
or
mation
a
s
ymm
e
tr
ic
a
nd,
in
thi
s
wa
y,
they
he
lp
in
the
pr
ice
dis
c
ove
r
y
of
B
it
c
oin
thus
im
pr
oving
mar
ke
t
e
f
f
icie
nc
y
a
nd
tr
a
ns
pa
r
e
nc
y
in
thi
s
mar
ke
t.
All
in
a
ll
,
s
tatis
ti
c
a
l
m
ode
ls
tend
to
take
les
s
ti
me
f
or
the
im
pleme
ntation
in
mos
t
of
the
c
a
s
e
s
whic
h
make
s
them
us
e
f
ul
whe
n
ti
m
e
is
the
c
ons
tr
a
int
.
None
thele
s
s
,
de
e
p
lea
r
ning
m
ode
ls
a
r
e
a
ble
to
he
lp
to
de
c
r
e
a
s
e
the
load
of
human
f
e
a
tur
e
e
nginee
r
ing
s
ince
they
a
r
e
a
ble
to
lea
r
n
a
ll
the
ne
c
e
s
s
a
r
y
f
e
a
tur
e
s
f
r
om
s
c
r
a
tch
f
r
om
r
a
w
da
ta
.
3.
1.
Gener
ali
z
e
d
au
t
or
e
gr
e
s
s
ive
c
on
d
it
ion
al
h
e
t
e
r
os
k
e
d
as
t
icit
y
(
GARC
H)
One
of
the
mos
t
a
dmi
r
e
d
e
c
onometr
ic
models
s
uit
a
ble
f
or
ti
me
s
e
r
ies
a
na
lys
is
a
nd
f
or
e
c
a
s
ti
ng
is
the
GA
R
C
H
model
f
or
thos
e
s
e
c
tor
s
whe
r
e
ther
e
is
a
volatil
it
y
c
lus
ter
ing
obs
e
r
ve
d.
R
e
c
ur
s
ively
a
djus
ti
ng
the
volatil
it
y
e
s
ti
mate
s
with
B
T
C
-
USD
da
ta
a
s
it
be
c
omes
a
c
c
e
s
s
ibl
e
is
one
wa
y
to
a
c
c
ompl
is
h
thi
s
.
F
igur
e
2
s
hows
the
GA
R
C
H
model
pr
ojec
ted
B
T
C
-
USD
pr
ice
[
13]
.
F
o
r
dis
tr
ibut
ion
of
log
r
e
tu
r
ns
=
log
(
−
1
)
,
=
−
−
1
[
]
is
the
mode
r
niza
ti
on
a
t
ti
me
.
B
y
including
=
+
a
t
t
i
me
,
whe
r
e
is
the
mea
n
c
ons
tant.
T
he
mathe
matica
l
f
or
mul
a
ti
on
of
GA
R
C
H
(
1,
1
)
model
is
given
in
(
1)
to
(
3)
.
F
igur
e
2.
GA
R
C
H
model
pr
e
dicte
d
B
T
C
-
USD
pr
ice
F
or
log
r
e
tur
ns
s
e
r
ies
=
−
−
1
[
]
be
the
innovation
.
T
he
n
f
o
ll
ows
a
GA
R
C
H
(
p,
q
)
in
mea
n
model
if
,
=
√
ℎ
(
1)
ℎ
=
0
+
∑
1
−
1
2
=
1
+
∑
1
ℎ
−
1
=
1
(
2)
√
ℎ
=
0
+
∑
1
=
1
(
|
−
1
|
-
η
1
−
1
)
+
∑
1
=
1
√
ℎ
−
1
(
3)
T
he
GA
R
C
H
(
,
)
model
is
s
tatic
if
,
∑
=
1
+
∑
=
1
≤
1
.
F
ur
ther
,
∑
=
1
+
∑
=
1
=
1
,
then
the
GA
R
C
H
(
,
)
pr
oc
e
s
s
is
int
e
gr
a
ted
GA
R
C
H
(
I
GA
R
C
H)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
B
it
c
oin
v
olat
il
it
y
for
e
c
as
ti
ng:
a
c
ompar
ati
v
e
analys
is
of
c
onv
e
nti
onal
…
(
N
r
us
ingha
T
r
ipat
hy
)
617
3.
2.
T
h
r
e
s
h
old
AR
CH
(
T
AR
CH)
T
he
inf
luenc
e
of
p
r
e
vious
volatil
it
y
s
hoc
ks
on
p
r
e
s
e
nt
volatil
it
y
is
incor
por
a
ted
int
o
the
T
AR
C
H
model,
whic
h
e
xpa
nds
upon
the
c
onve
nti
ona
l
GA
R
C
H
model.
E
qua
ti
on
(
4
)
p
r
e
s
e
nts
the
f
un
da
menta
l
e
qua
ti
on
of
the
T
AR
C
H
(
,
)
model.
2
=
+
−
1
2
+
−
1
2
+
−
1
2
. 1
{
−
1
<
0
}
(
4)
H
e
r
e
2
is
the
c
onve
nti
ona
l
va
r
ianc
e
of
the
ti
me
s
e
r
ies
a
t
ti
me
t,
is
the
c
ons
tant
ter
m
,
,
,
a
nd
is
the
c
oe
f
f
icie
nt
of
the
lagge
d
e
r
r
or
ter
m
[
14]
.
T
he
T
AR
C
H
model
a
ll
ows
c
a
ptur
ing
the
a
s
ymm
e
tr
ic
r
e
tor
t
of
f
luctua
ti
on
to
s
hoc
ks
,
both
pos
it
ive
a
nd
ne
ga
ti
ve
by
the
ter
m
−
1
2
.
1
{
−
1
<
0
}.
T
his
ter
m
a
djus
ts
the
c
ondit
ional
va
r
ianc
e
ba
s
e
d
on
the
s
ign
o
f
the
lagg
e
d
s
qua
r
e
d
e
r
r
or
ter
m
−
1
2
.
T
he
T
AR
C
H
model's
a
bil
it
y
to
a
c
c
ount
f
or
a
s
ymm
e
tr
ic
volatil
it
y
im
pa
c
ts
is
one
of
it
s
main
f
e
a
tur
e
s
.
Give
n
that
ma
r
ke
t
s
e
nti
ment
c
ha
nge
s
quickly
a
nd
pr
ice
moveme
nts
f
r
e
que
ntl
y
s
how
a
s
ymm
e
tr
y
in
the
c
ontext
of
B
it
c
oin,
the
T
AR
C
H
model's
c
a
pa
c
it
y
to
indepe
nde
ntl
y
r
e
pr
e
s
e
nt
pos
it
ive
a
nd
n
e
ga
ti
ve
volatil
it
y
s
hoc
ks
c
a
n
lea
d
to
mo
r
e
p
r
e
c
is
e
f
or
e
c
a
s
ts
.
F
igur
e
3
s
hows
the
T
AR
C
H
model
f
o
r
e
c
a
s
t
B
T
C
-
USD
pr
ice
[
15
]
,
[
16]
.
F
igur
e
3.
T
AR
C
H
model
pr
e
dicte
d
B
T
C
-
USD
pr
ic
e
3.
3.
L
on
g
s
h
or
t
-
t
e
r
m
m
e
m
or
y
(
L
S
T
M
)
B
it
c
o
in
p
r
ic
e
da
ta
o
f
t
e
n
e
xh
ib
i
ts
l
on
g
-
te
r
m
r
e
lat
i
ons
h
i
ps
a
n
d
i
nt
r
ic
a
te
pa
tt
e
r
ns
,
w
h
ich
c
a
n
lea
d
t
o
m
o
r
e
a
c
c
u
r
a
te
f
or
e
c
a
s
ts
o
f
f
u
tu
r
e
pr
ic
e
va
r
iat
i
ons
.
T
h
e
s
e
c
om
p
lex
c
o
r
r
e
l
a
t
io
ns
w
it
h
B
i
tc
oi
n
va
lu
e
s
a
r
e
e
f
f
e
c
t
ive
ly
m
o
de
led
us
i
ng
L
S
T
M
m
od
e
ls
.
L
S
T
M
s
a
r
e
po
we
r
f
ul
n
on
li
ne
a
r
f
u
nc
ti
on
a
pp
r
ox
im
a
t
or
s
th
a
t
e
n
ha
nc
e
the
r
e
li
a
b
il
i
ty
o
f
p
r
e
d
ic
ti
on
s
.
I
n
t
his
s
tu
dy
,
a
n
L
S
T
M
l
a
y
e
r
wi
t
h
20
un
it
s
is
e
mp
lo
ye
d
,
u
ti
li
z
i
ng
in
pu
t
s
e
q
ue
nc
e
s
s
pa
n
ni
ng
14
da
ys
(
or
14
-
ti
me
s
teps
)
a
nd
c
o
r
r
e
s
po
ndi
n
g
ta
r
ge
t
va
lu
e
s
.
T
hi
s
la
ye
r
c
a
pt
u
r
e
s
a
nd
p
r
oc
e
s
s
e
s
t
e
mp
or
a
l
d
e
p
e
n
de
n
c
i
e
s
f
r
o
m
t
he
in
pu
t
s
e
qu
e
nc
e
s
.
F
i
gu
r
e
4
i
l
lus
t
r
a
tes
th
e
L
S
T
M
mo
de
l's
f
o
r
e
c
a
s
t
o
f
B
T
C
-
U
S
D
p
r
i
c
e
s
[
1
7
]
,
[
1
8]
.
T
he
ma
th
e
ma
t
ica
l
f
o
r
mu
la
ti
ons
o
f
t
he
ba
s
ic
L
S
T
M
m
od
e
l
a
r
e
p
r
e
s
e
n
te
d
i
n
(
5
)
t
o
(
7
)
.
=
(
.
[
ℎ
−
1
,
]
+
)
(
5)
=
(
.
[
ℎ
−
1
,
]
+
)
(
6)
=
∗
−
1
+
∗
ta
nh
(
.
[
ℎ
−
1
,
]
+
)
(
7)
whe
r
e
,
,
a
nd
indi
c
a
te
that
the
inpu
t,
output
,
a
nd
f
or
ge
t
ga
tes
a
r
e
a
c
ti
va
ted.
a
nd
ℎ
de
note
the
a
c
ti
va
ti
on
ve
c
tor
.
3.
4.
B
id
ire
c
t
ion
al
L
S
T
M
(
B
i
-
L
S
T
M
)
T
o
im
pr
ove
the
model's
a
bil
it
y
to
de
tec
t
tempo
r
a
l
tr
e
nds
,
we
e
mpl
oy
a
B
i
-
L
S
T
M
a
r
c
hit
e
c
tur
e
that
c
a
ptur
e
s
da
ta
f
r
om
both
pr
e
c
e
ding
a
nd
s
ubs
e
q
ue
nt
ti
me
s
teps
.
T
he
ini
ti
a
l
bidi
r
e
c
ti
ona
l
L
S
T
M
laye
r
,
c
ompr
is
ing
32
unit
s
a
nd
r
e
tu
r
ning
s
e
que
nc
e
s
,
f
a
c
i
li
tate
s
inf
or
mation
p
r
opa
ga
ti
on
to
s
ubs
e
que
nt
laye
r
s
while
pr
e
s
e
r
ving
tempor
a
l
c
ontext.
A
s
e
c
ond
bidi
r
e
c
ti
o
na
l
L
S
T
M
laye
r
with
16
unit
s
int
e
g
r
a
tes
da
ta
f
r
om
both
dir
e
c
ti
ons
.
T
he
f
inal
de
ns
e
laye
r
,
e
quipped
with
a
s
ingl
e
ne
ur
on,
pr
e
dicts
the
B
it
c
oin
pr
ice
.
T
he
s
im
pli
f
ied
Bi
-
L
S
T
M
model
is
mathe
matica
ll
y
r
e
pr
e
s
e
nted
in
(
8)
a
nd
(
9)
.
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
614
-
623
618
=
(
[
ℎ
−
1
,
]
+
)
(
8)
=
(
[
ℎ
−
1
,
]
+
)
(
9)
Ac
c
or
ding
to
(
8)
a
nd
(
9
)
,
whe
r
e
,
is
the
input
ve
c
tor
,
ℎ
is
the
hidden
s
tate
ve
c
tor
.
F
igur
e
5
s
hows
the
Bi
-
L
S
T
M
model
p
r
e
dicte
d
B
T
C
-
USD
pr
ice
.
T
he
mar
ke
tpl
a
c
e
s
f
o
r
c
r
yptocur
r
e
nc
ies
a
r
e
e
xtr
e
mel
y
volatil
e
a
nd
pr
one
to
s
udde
n
s
hif
ts
ove
r
ti
me
.
B
e
c
a
us
e
bidi
r
e
c
ti
ona
l
L
S
T
M
s
c
a
n
c
a
ptur
e
long
-
r
a
nge
r
e
lations
hips
a
nd
modi
f
y
their
int
e
r
na
l
s
tate
s
in
r
e
s
pons
e
to
pa
s
t
a
nd
f
utu
r
e
da
ta,
they
a
r
e
e
xc
e
ll
e
nt
a
t
r
e
pr
e
s
e
nti
ng
tempor
a
l
dyna
mi
c
s
.
As
a
r
e
s
ult
,
the
model
c
a
n
a
djus
t
to
s
hif
t
ing
mar
ke
t
c
ondit
ions
a
nd
p
r
oduc
e
pr
e
c
is
e
f
or
e
c
a
s
ts
ove
r
a
r
a
nge
of
t
im
e
pe
r
iods
[
19]
,
[
20
]
.
F
igur
e
4.
L
S
T
M
model
pr
e
dicte
d
B
T
C
-
USD
pr
ice
F
igur
e
5.
B
idi
r
e
c
ti
ona
l
L
S
T
M
model
pr
e
dicte
d
B
T
C
-
USD
pr
ice
3.
5
.
M
u
lt
ivariat
e
B
i
-
L
S
T
M
M
ult
ivar
iate
B
i
-
L
S
T
M
s
e
xc
e
l
a
t
c
a
ptur
ing
thes
e
r
e
lations
hips
by
pr
oc
e
s
s
ing
input
s
both
f
o
r
wa
r
d
a
nd
ba
c
kwa
r
d
[
21]
.
T
he
pr
e
dicte
d
pr
ice
o
f
B
T
C
-
USD
a
s
pe
r
the
mul
ti
va
r
iate
B
i
-
L
S
T
M
model
is
a
s
s
hown
be
low
in
F
igur
e
6.
M
ult
ivar
iate
B
i
-
L
S
T
M
s
a
r
e
a
ls
o
mor
e
be
ne
f
icia
l
in
lea
r
n
ing
the
tempor
a
l
c
ha
r
a
c
ter
is
ti
c
s
of
da
ta
s
ince
it
us
e
s
pa
s
t
a
nd
f
utur
e
in
f
or
mation
dur
ing
lea
r
ning.
T
his
a
ppr
oa
c
h
is
ve
r
y
us
e
f
ul
f
or
B
T
C
f
o
r
e
c
a
s
ti
ng
a
s
his
tor
ica
l
is
known
f
or
boos
ti
ng
the
pr
e
dictive
po
tential
[
22]
.
F
unda
menta
l
mul
ti
va
r
iate
B
i
-
L
S
T
M
model
is
mathe
matica
ll
y
c
ha
r
a
c
ter
ize
d
in
(
10
)
to
(
15)
:
=
(
[
ℎ
−
1
,
]
+
)
(
10)
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
B
it
c
oin
v
olat
il
it
y
for
e
c
as
ti
ng:
a
c
ompar
ati
v
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analys
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onv
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nti
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…
(
N
r
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ingha
T
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ipat
hy
)
619
=
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[
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−
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+
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(
11)
̃
=
ℎ
(
[
ℎ
−
1
,
]
+
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(
12)
=
ʘ
−
1
+
ʘ
̃
(
13)
=
(
[
ℎ
−
1
,
]
+
)
(
14)
ℎ
=
ʘ
ta
nh
(
)
(
15)
whe
r
e
is
the
input
ve
c
tor
a
t
ti
me
s
tep
,
ℎ
is
the
hi
dde
n
s
tate
a
t
ti
me
,
is
the
c
e
ll
s
tate
,
a
nd
a
s
we
ight
matr
ice
s
a
nd
a
s
the
bias
ve
c
tor
.
L
S
T
M
s
c
a
n
lea
r
n
r
e
pr
e
s
e
ntations
of
the
input
da
ta
a
t
dif
f
e
r
e
n
t
leve
ls
of
a
bs
tr
a
c
ti
on
a
nd
he
nc
e
r
e
ve
a
l
inf
o
r
mation
a
bou
t
wha
t
a
r
e
the
unde
r
lyi
ng
r
e
a
s
ons
dr
ivi
ng
f
luctua
ti
ons
in
B
it
c
oin's
pr
ice
in
s
tanda
r
d
r
e
gular
it
y.
T
he
int
e
r
p
r
e
tabili
ty
c
a
n
be
us
e
f
ul
f
or
both
making
int
e
ll
igen
t
tr
a
ding
de
c
is
ions
a
s
we
ll
a
s
ha
ving
a
n
unde
r
s
tanding
of
m
a
r
ke
t
dyna
mi
c
s
[
23]
–
[
25
]
.
F
igur
e
6.
M
ult
ivar
iate
B
i
-
L
S
T
M
model
f
o
r
e
c
a
s
t
B
T
C
-
USD
pr
ice
4.
RE
S
UL
T
AN
AL
YS
I
S
T
r
a
de
r
s
a
nd
inves
tor
s
r
e
ly
on
volatil
it
y
f
o
r
e
c
a
s
ts
a
s
im
por
tant
tool
s
in
de
a
li
ng
with
r
is
ks
mor
e
e
f
f
icie
ntl
y
[
26
]
.
T
he
e
r
r
o
r
s
c
or
e
s
f
r
o
m
T
a
ble
1
c
ompar
e
dif
f
e
r
e
nt
models
us
e
d
to
pr
e
dict
B
it
c
oin
volatil
it
y.
GA
R
C
H
model’
s
e
r
r
or
metr
ics
a
r
e
higher
with
r
oot
mea
n
s
qua
r
e
d
e
r
r
or
(
R
M
S
E
)
of
0
.
1930
a
nd
r
oot
mea
n
s
qua
r
e
pe
r
c
e
ntage
e
r
r
or
(
R
M
S
P
E
)
o
f
0.
5334
,
ind
ica
ti
ng
that
it
is
not
good
a
t
c
a
ptur
ing
the
int
r
ica
te
pa
tt
e
r
ns
of
B
it
c
oin’
s
volatil
it
y
c
or
r
e
c
tl
y.
On
the
othe
r
ha
nd,
T
AR
C
H
ha
s
im
pr
ove
d
s
igni
f
ica
ntl
y
e
videnc
e
d
by
a
n
R
M
S
E
of
0.
0702
a
nd
R
M
S
P
E
of
0.
1752
whic
h
indi
c
a
tes
a
be
tt
e
r
f
it
to
bit
c
oin
’
s
a
s
ymm
e
tr
ic
volatil
it
y
c
ha
r
a
c
ter
is
ti
c
s
whe
n
c
ompar
e
d
to
GA
R
C
H.
W
he
n
c
omi
ng
to
de
e
p
lea
r
ning
models
,
L
S
T
M
s
hows
a
much
-
e
nha
nc
e
d
pe
r
f
or
manc
e
ha
ving
a
n
R
M
S
E
va
lue
of
0
.
0448
a
n
d
R
M
S
P
E
va
lue
of
0.
1155
whic
h
s
ur
pa
s
s
e
s
thos
e
f
or
both
GA
R
C
H
a
nd
T
AR
C
H
models
a
li
ke
.
T
he
B
i
-
L
S
T
M
model,
on
the
o
ther
ha
nd
,
p
r
oduc
e
s
c
ompetit
iv
e
r
e
s
ult
s
with
a
n
R
M
S
E
of
0.
0519
a
nd
a
n
R
M
S
P
E
of
0.
1288,
indi
c
a
ti
ng
bid
ir
e
c
ti
ona
l
da
ta
p
r
oc
e
s
s
in
g,
whic
h
s
tr
e
ngthens
it
s
c
a
pa
c
it
y
f
or
making
pr
e
dictions
.
B
ut
the
incor
por
a
ti
on
of
s
e
ve
r
a
l
pr
e
dictor
s
,
the
M
ul
ti
va
r
iate
Bi
-
L
S
T
M
model
r
e
c
or
ds
a
lowe
r
e
r
r
o
r
s
c
or
e
:
R
M
S
E
=
0.
0425;
R
M
S
P
E
=
0.
1106.
T
his
mea
ns
that
it
is
mor
e
a
c
c
ur
a
te
in
f
or
e
c
a
s
ti
ng
the
f
utu
r
e
va
lues
of
B
it
c
oi
n
volatil
it
y
.
T
his
wor
k
s
he
ds
li
ght
on
the
potentia
l
us
e
o
f
de
e
p
lea
r
ning
s
ys
tems
f
o
r
digi
tal
c
ur
r
e
nc
y
f
or
e
c
a
s
ti
ng,
s
ince
they
c
a
n
p
r
ovide
va
luable
ins
ight
s
int
o
r
is
k
mana
ge
ment
a
nd
inves
tm
e
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he
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ha
oti
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f
inanc
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mar
ke
ts
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T
a
ble
1.
E
r
r
or
s
c
or
e
of
e
a
c
h
model
M
ode
l
n
a
me
R
M
S
E
R
M
S
P
E
G
A
R
C
H
0.1930
0.5334
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R
C
H
0.0702
0.1752
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M
0.0448
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Bi
-
L
S
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M
M
ul
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va
r
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te
B
i
-
L
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T
M
0.0519
0.0425
0.1288
0.1106
Evaluation Warning : The document was created with Spire.PDF for Python.
I
S
S
N
:
2088
-
8708
I
nt
J
E
lec
&
C
omp
E
ng
,
Vol
.
15
,
No.
1
,
F
e
br
ua
r
y
20
25
:
614
-
623
620
A
ba
r
diagr
a
m
c
ompar
ing
the
R
M
S
E
a
nd
R
M
S
P
E
s
c
or
e
s
of
e
s
ti
mate
d
va
lues
a
ga
ins
t
a
c
tual
va
lues
f
r
om
dif
f
e
r
e
nt
models
wa
s
s
hown
in
F
igu
r
e
7
,
w
hich
pr
e
s
e
nts
a
vis
ua
l
r
e
pr
e
s
e
ntation
o
f
how
a
c
c
u
r
a
te
a
nd
r
e
li
a
ble
e
a
c
h
model
is
whe
n
c
ompar
e
d
to
one
a
n
other
.
As
s
hown
in
thi
s
f
igur
e
,
the
mul
ti
va
r
iate
B
i
-
L
S
T
M
model
ha
s
a
low
R
M
S
E
a
nd
R
M
S
P
E
s
c
or
e
.
T
he
m
ult
ivar
iate
B
i
-
L
S
T
M
model’
s
R
M
S
E
s
c
or
e
is
0.
04
25
while
the
R
M
S
P
E
s
c
or
e
is
0
.
1106.
W
e
take
a
va
r
iable
_
while
a
s
s
igni
ng
it
a
6
.
9e
-
5
va
lue.
T
he
lea
r
ning
r
a
t
e
r
e
pr
e
s
e
nted
by
thi
s
number
,
6
.
9e
-
5,
is
c
omm
onl
y
e
mpl
oye
d
in
de
e
p
lea
r
ning
methods
.
S
pe
c
if
ica
ll
y,
it
is
uti
li
z
e
d
in
gr
a
dient
de
s
c
e
nt
a
nd
other
opti
mi
z
a
ti
on
tec
hniques
to
de
f
ine
the
s
tep
s
ize
c
hos
e
n
dur
ing
e
a
c
h
it
e
r
a
ti
on
of
upda
ti
ng
the
model
pa
r
a
mete
r
s
.
I
n
th
is
ins
tanc
e
,
6.
9e
-
5
is
wr
it
ten
in
s
c
ientif
ic
notation,
whe
r
e
e
-
5
s
tands
f
or
6.
9
ti
mes
10
r
a
is
e
d
to
the
powe
r
of
-
5.
6
.
9e
-
5
is
ther
e
f
or
e
e
qua
l
to
0.
000069
.
F
o
r
e
c
a
s
ti
ng
volatil
it
y
ha
s
a
n
im
pa
c
t
on
how
wide
ly
c
r
yptocur
r
e
nc
ies
a
r
e
us
e
d
f
or
r
e
gular
tr
a
ns
a
c
ti
ons
a
nd
a
ppli
c
a
ti
ons
.
I
f
the
va
lue
of
c
r
yp
tocur
r
e
nc
ies
f
luctua
tes
a
lot
,
pe
ople
c
ould
be
r
e
lucta
nt
to
a
c
c
e
pt
them
a
s
pa
yme
nt
or
us
e
them
a
s
a
mea
ns
of
e
xc
ha
nge
.
M
or
e
pr
e
c
is
e
f
o
r
e
c
a
s
ts
of
volatil
i
ty
r
e
duc
e
thi
s
wor
r
y
a
nd
e
nc
our
a
ge
br
oa
de
r
us
e
.
F
igur
e
8
s
hows
the
tr
a
ini
ng
M
S
E
vs
tr
a
ini
ng
R
M
S
P
E
plot
.
F
igur
e
7.
His
togr
a
m
plo
t
of
R
M
S
E
a
nd
R
M
S
P
E
of
e
a
c
h
model
F
igur
e
8.
T
r
a
ini
ng
M
S
E
vs
t
r
a
in
ing
R
M
S
P
E
plot
5.
CONC
L
USI
ON
W
e
ha
ve
e
xa
mi
ne
d
a
nd
pr
ojec
ted
f
inanc
ial
ti
me
s
e
r
ies
r
e
late
d
to
c
r
yptocu
r
r
e
nc
ies
,
p
r
im
a
r
il
y
c
onc
e
ntr
a
ti
ng
on
B
it
c
oin
,
the
mos
t
r
e
c
ognize
d
s
pe
c
im
e
n
of
th
is
kind
of
digi
tal
a
s
s
e
t.
Our
a
pp
r
o
a
c
h
us
e
s
mul
ti
va
r
iate
B
i
-
L
S
T
M
models
,
whic
h
a
r
e
a
de
pt
a
t
mer
ging
his
tor
ica
l
a
nd
r
e
a
l
-
ti
me
da
ta
,
to
f
a
mi
li
a
r
ize
the
s
hif
ti
ng
mar
ke
t
c
ondit
ions
.
W
e
s
how
how
thes
e
models
c
a
n
de
tec
t
a
nomalies
a
nd
f
o
r
e
s
e
e
potential
is
s
ue
s
,
im
pr
oving
r
e
li
a
bil
it
y
a
nd
tr
a
ns
pa
r
e
nc
y
in
c
r
ypto
c
ur
r
e
nc
y
tr
a
ding.
P
r
e
c
is
e
ly
f
or
e
c
a
s
ti
ng
the
f
luctu
a
ti
ons
in
B
it
c
oin
c
a
n
im
pa
c
t
not
jus
t
pa
r
ti
c
ular
tr
a
ding
s
tr
a
tegie
s
but
a
ls
o
br
oa
de
r
e
leme
nts
s
uc
h
a
s
e
nha
n
c
e
d
r
is
k
mi
ti
ga
ti
on
a
nd
in
f
or
med
mar
ke
t
gove
r
na
nc
e
.
M
ode
r
n
a
na
lyt
ica
l
methods
a
nd
de
e
p
lea
r
ning
mo
de
ls
li
ke
Evaluation Warning : The document was created with Spire.PDF for Python.
I
nt
J
E
lec
&
C
omp
E
ng
I
S
S
N:
2088
-
8708
B
it
c
oin
v
olat
il
it
y
for
e
c
as
ti
ng:
a
c
ompar
ati
v
e
analys
is
of
c
onv
e
nti
onal
…
(
N
r
us
ingha
T
r
ipat
hy
)
621
Bi
-
L
S
T
M
s
of
f
e
r
s
take
holder
s
c
r
uc
ial
ins
tr
ume
nts
f
or
ha
ndli
ng
c
ompl
e
x
mar
ke
t
c
ondit
ions
a
s
the
c
r
yptocur
r
e
nc
y
e
c
os
ys
tem
e
volves
.
F
utur
e
s
tudi
e
s
c
ould
f
oc
us
on
e
nha
nc
ing
the
model's
f
unc
ti
ona
li
t
y,
a
dding
mor
e
da
ta
s
our
c
e
s
f
or
incr
e
a
s
e
d
pr
e
dictive
a
c
c
ur
a
c
y,
de
ve
lopi
ng
r
e
a
l
-
ti
me
moni
to
r
ing
s
ys
tems
,
e
xplor
ing
e
f
f
e
c
ti
ve
r
is
k
mana
ge
ment
s
tr
a
tegie
s
,
a
nd
e
xa
m
ini
ng
the
r
e
gulato
r
y
im
pli
c
a
ti
ons
o
f
volatil
i
ty
f
or
e
c
a
s
ts
.
T
hr
ough
thes
e
e
f
f
or
ts
,
we
s
e
e
k
to
incr
e
a
s
e
our
un
de
r
s
tanding
of
B
it
c
oin
mar
ke
ts
a
nd
e
s
tablis
h
a
mo
r
e
s
table
a
nd
r
obus
t
e
nvir
onment
f
or
digi
tal
a
s
s
e
ts
.
RE
F
E
RE
NC
E
S
[
1]
V
.
D
e
r
be
nt
s
e
v,
A
.
M
a
tv
iy
c
huk,
a
nd
V
.
N
.
S
ol
ovi
e
v,
“
F
or
e
c
a
s
ti
ng
of
c
r
ypt
oc
u
r
r
e
nc
y
pr
ic
e
s
us
in
g
ma
c
hi
ne
le
a
r
ni
ng,”
A
dv
an
c
e
d
St
udi
e
s
of
F
in
anc
ia
l
T
e
c
hnol
ogi
e
s
and C
r
y
pt
oc
ur
r
e
nc
y
M
ar
k
e
ts
, pp. 211
–
231, 2020, doi:
10.1007/978
-
981
-
15
-
4498
-
9_12.
[
2]
N
.
T
r
ip
a
th
y,
S
.
H
ot
a
,
a
nd
D
.
M
i
s
hr
a
,
“
P
e
r
f
or
ma
nc
e
a
na
ly
s
is
o
f
bi
tc
oi
n
f
or
e
c
a
s
ti
ng
us
in
g
de
e
p
le
a
r
ni
ng
te
c
hni
que
s
,”
I
ndone
s
ia
n
J
our
nal
of
E
le
c
tr
ic
al
E
ngi
ne
e
r
in
g
and
C
om
put
e
r
Sc
i
e
nc
e
,
vol
.
31,
no.
3,
pp.
1515
–
1522,
S
e
p.
2023,
doi
:
10.11591/i
je
e
c
s
.v31.i3.pp1515
-
1522.
[
3]
C
.
C
onr
a
d,
A
.
C
us
to
vi
c
,
a
nd
E
.
G
hys
e
ls
,
“
L
ong
-
a
nd
s
hor
t
-
te
r
m
c
r
ypt
oc
ur
r
e
nc
y
vol
a
ti
li
ty
c
ompone
nt
s
:
A
G
A
R
C
H
-
M
I
D
A
S
a
na
ly
s
is
,”
J
our
nal
of
R
is
k
and F
in
anc
ia
l
M
anage
m
e
nt
, vol
. 11, no. 2, M
a
y 2018, doi:
10.3390/j
r
f
m11020023.
[
4]
A
.
N
gunyi,
S
.
M
undi
a
,
a
nd
C
.
O
ma
r
i,
“
M
ode
ll
in
g
vol
a
ti
li
ty
dyna
mi
c
s
of
c
r
ypt
oc
ur
r
e
nc
ie
s
us
in
g
G
A
R
C
H
mode
ls
,
”
J
our
n
al
of
M
at
he
m
at
ic
al
F
in
anc
e
, vol
. 09, no. 04, pp. 591
–
615, 2019, doi:
10.4236/j
mf
.2019.94030.
[
5]
B
.
P
odgor
e
le
c
,
M
.
T
ur
ka
novi
ć
,
a
nd
S
.
K
a
r
a
k
a
ti
č
,
“
A
ma
c
hi
ne
le
a
r
ni
ng
-
ba
s
e
d
me
th
od
f
or
a
ut
oma
te
d
bl
oc
kc
ha
in
tr
a
ns
a
c
ti
on
s
ig
ni
ng i
nc
lu
di
ng pe
r
s
ona
li
z
e
d a
noma
ly
de
t
e
c
ti
on,”
Se
n
s
or
s
(
S
w
it
z
e
r
la
nd)
, vol
. 20, no. 1, 2020, doi
:
10.3390/s
20010147.
[
6]
K
.
A
r
iy
a
,
S
.
C
ha
na
im
,
a
nd
A
.
Y
.
D
a
w
od,
“
C
or
r
e
la
ti
on
be
tw
e
e
n
c
a
pi
ta
l
ma
r
ke
ts
a
nd
c
r
ypt
oc
ur
r
e
nc
y:
im
pa
c
t
of
th
e
c
or
ona
vi
r
us
,”
I
nt
e
r
nat
io
nal
J
our
nal
of
E
le
c
t
r
ic
al
and
C
om
put
e
r
E
ngi
ne
e
r
in
g
,
vol
.
13,
no.
6,
pp.
6637
–
6645,
2023,
doi
:
10.11591/i
je
c
e
.v13i6.pp6637
-
6645.
[
7]
A
.
V
is
w
a
m
a
nd
G
.
D
a
r
s
a
n,
“
A
n
e
f
f
ic
ie
nt
bi
tc
oi
n
f
r
a
ud
de
te
c
ti
on
in
s
oc
ia
l
me
di
a
ne
twor
ks
,”
in
P
r
oc
e
e
di
ng
s
of
I
E
E
E
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on C
ir
c
ui
t,
P
ow
e
r
and C
om
put
in
g T
e
c
hnol
ogi
e
s
, 20
17, pp. 1
–
4, doi:
10.1109/I
C
C
P
C
T
.2017.8074262.
[
8]
N
.
T
r
ip
a
th
y,
S
.
H
ot
a
,
S
.
P
r
us
ty
,
a
nd
S
.
K
.
N
a
ya
k,
“
P
e
r
f
or
ma
nc
e
a
na
ly
s
i
s
of
d
e
e
p
le
a
r
ni
ng
te
c
hni
que
s
f
or
ti
me
s
e
r
ie
s
f
or
e
c
a
s
ti
ng,”
in
2023
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
in
A
dv
anc
e
s
in
P
ow
e
r
,
Si
gn
al
,
and
I
nf
or
m
at
io
n
T
e
c
hnol
ogy
,
A
P
SI
T
2023
,
2023,
pp.
639
–
644,
doi
:
10.1109/AP
S
I
T
58554.2023.10201734.
[
9]
R
.
T
a
n,
Q
.
T
a
n,
P
.
Z
ha
ng,
a
nd
Z
.
L
i,
“
G
r
a
ph
ne
ur
a
l
ne
twor
k
f
or
e
th
e
r
e
um
f
r
a
ud
de
te
c
ti
o
n,”
in
P
r
oc
e
e
di
ngs
-
12
th
I
E
E
E
I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on B
ig
K
now
le
dge
, I
C
B
K
2021
, 2021,
pp. 78
–
85, doi:
10.1109/I
C
K
G
52313.2021.00020.
[
10]
R
.
F
.
I
br
a
hi
m,
A
.
M
.
E
li
a
n,
a
nd
M
.
A
ba
bne
h,
“
I
ll
ic
it
a
c
c
ount
d
e
te
c
ti
on
in
th
e
E
th
e
r
e
um
B
lo
c
kc
ha
in
us
in
g
ma
c
hi
ne
l
e
a
r
ni
ng,”
in
2021 I
nt
e
r
nat
io
nal
C
onf
e
r
e
nc
e
on I
nf
or
m
at
io
n T
e
c
hnol
ogy
,
2021, pp. 488
–
493, doi:
10.1109/I
C
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bi
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d
A
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ti
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“
D
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c
ti
on
of
P
onz
i
s
c
he
me
on
E
th
e
r
e
um
us
in
g
ma
c
hi
ne
l
e
a
r
ni
ng a
lg
or
it
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,”
Sc
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nt
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ba
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d
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s
s
if
ic
a
ti
on
a
nd
de
te
c
ti
on
a
p
pr
oa
c
h
f
or
E
th
e
r
e
um
s
ma
r
t
c
ont
r
a
c
t,
”
I
nf
or
m
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N
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A
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M
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“
A
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f
r
a
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f
or
f
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a
ud
de
te
c
ti
on
in
bi
t
c
oi
n
tr
a
ns
a
c
ti
ons
th
r
ough
e
n
s
e
mbl
e
s
ta
c
ki
ng
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it
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E
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r
ic
a
l
f
or
e
c
a
s
ti
ng a
na
ly
s
is
of
bi
tc
oi
n pr
ic
e
s
:
a
c
ompa
r
is
on of
ma
c
hi
ne
le
a
r
ni
ng,
de
e
p
le
a
r
ni
ng,
a
nd
e
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e
mbl
e
le
a
r
ni
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,”
I
nt
e
r
nat
io
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J
our
nal
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le
c
tr
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C
om
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r
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g
Sy
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dy
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nd
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di
c
ti
on
of
bi
tc
oi
n
pr
ic
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s
w
it
h
B
a
ye
s
ia
n
ne
ur
a
l
n
e
twor
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ba
s
e
d
on
B
lo
c
kc
ha
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di
t
c
a
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d
f
r
a
ud
de
te
c
ti
on
u
s
in
g
lo
gi
s
ti
c
r
e
gr
e
s
s
i
on
a
nd
s
ynt
he
ti
c
mi
nor
it
y
ove
r
s
a
mpl
in
g
te
c
hni
que
(
S
M
O
T
E
)
a
ppr
oa
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h,”
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nt
e
r
nat
io
nal
J
our
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om
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ng
c
r
ypt
oc
ur
r
e
nc
y
r
e
tu
r
ns
a
nd
vol
ume
us
in
g
s
e
a
r
c
h
e
ngi
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,”
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ia
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ng
c
r
ypt
oc
ur
r
e
nc
y
pr
ic
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s
us
in
g
r
e
c
ur
r
e
nt
ne
ur
a
l
ne
twor
k
a
nd
lo
ng
s
hor
t
-
te
r
m
me
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y,”
D
at
a
and
K
now
le
dge
E
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a
s
ti
ng
a
nd
tr
a
di
ng
c
r
ypt
oc
ur
r
e
nc
ie
s
w
it
h
ma
c
hi
ne
le
a
r
ni
ng
und
e
r
c
ha
ngi
ng
m
a
r
ke
t
c
ondi
ti
ons
,”
F
in
anc
ia
l
I
nnov
at
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oc
ur
r
e
nc
y
di
r
e
c
ti
on
f
or
e
c
a
s
ti
ng
u
s
in
g
de
e
p
le
a
r
ni
ng
a
lg
or
it
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,”
J
ou
r
nal
of
St
at
is
ti
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al
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om
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ve
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T
he
pr
e
di
c
ti
ve
pow
e
r
of
publ
ic
T
w
it
te
r
s
e
nt
im
e
nt
f
or
f
or
e
c
a
s
ti
ng
c
r
ypt
oc
ur
r
e
nc
y
pr
ic
e
s
,”
J
our
nal
of
I
nt
e
r
nat
io
nal
F
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l
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C
r
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oc
ur
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nc
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f
r
a
ud
de
te
c
ti
on
th
r
ough
c
la
s
s
if
ic
a
ti
on
te
c
hni
que
s
,
”
I
nt
e
r
nat
io
nal
J
our
nal
of
E
le
c
t
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and
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“
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s
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c
r
ypt
oc
ur
r
e
nc
y
p
r
ic
e
us
in
g
c
onvolut
i
ona
l
ne
ur
a
l
ne
twor
ks
w
it
h
w
e
ig
ht
e
d
a
nd
a
tt
e
nt
iv
e
me
mor
y
c
ha
nne
ls
,”
E
x
pe
r
t
Sy
s
te
m
s
w
it
h
A
ppl
ic
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io
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A
f
if
,
a
nd
A
.
R
ukmi
na
s
t
it
i
M
a
s
yr
if
a
h,
“
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ompa
r
a
ti
ve
s
tu
dy
f
or
B
it
c
oi
n
c
r
ypt
oc
ur
r
e
nc
y
f
or
e
c
a
s
ti
ng
in
pe
r
io
d
2017
-
2019,”
J
our
nal
of
P
hy
s
ic
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e
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nc
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Se
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s
la
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“
B
it
c
oi
n
F
or
e
c
a
s
ti
ng
us
in
g
A
R
I
M
A
a
nd
P
R
O
P
H
E
T
,”
in
U
B
M
K
2018
-
3r
d I
nt
e
r
nat
io
nal
C
onf
e
r
e
n
c
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Sc
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a
hma
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S
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“
P
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di
c
ti
ng
a
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f
or
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c
a
s
ti
ng
th
e
pr
ic
e
of
c
on
s
ti
tu
e
nt
s
a
nd
in
de
x of
c
r
ypt
oc
ur
r
e
nc
y us
in
g ma
c
hi
ne
l
e
a
r
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ng,”
ar
X
iv
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8444.
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