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av
e
b
ee
n
u
s
ed
f
o
r
n
etwo
r
k
tr
af
f
ic
an
a
ly
s
is
an
d
f
o
r
ec
asti
n
g
,
s
u
c
h
as
tim
e
s
er
ies
m
o
d
els,
m
o
d
e
r
n
d
ata
m
in
in
g
tech
n
iq
u
es,
m
ac
h
in
e
l
ea
r
n
i
n
g
(
ML
)
,
an
d
h
y
b
r
id
tech
n
iq
u
es.
T
h
e
m
ain
f
o
c
u
s
o
f
th
is
p
ap
e
r
is
o
n
h
y
b
r
id
m
ac
h
in
e
lea
r
n
in
g
-
b
ased
f
r
am
ewo
r
k
s
.
Gen
er
ally
,
ML
tech
n
iq
u
es
ar
e
u
s
ed
in
v
a
r
io
u
s
d
o
m
ain
s
to
s
o
lv
e
v
ar
i
o
u
s
co
m
p
lex
p
r
o
b
le
m
s
in
clu
d
in
g
o
p
tim
izatio
n
r
eso
u
r
ce
m
a
n
ag
em
e
n
t,
allo
ca
tio
n
,
an
d
a
u
to
m
atio
n
.
M
L
ap
p
licatio
n
s
ar
e
also
u
s
ed
i
n
co
m
m
u
n
icatio
n
n
etwo
r
k
s
.
T
h
e
ap
p
licatio
n
o
f
ML
h
as
r
ec
o
r
d
ed
an
u
n
p
r
ec
ed
en
ted
s
u
r
g
e
in
co
m
m
u
n
icatio
n
n
etwo
r
k
s
.
ML
en
ab
les
a
s
y
s
tem
to
s
u
m
m
ar
ize
an
d
ab
s
tr
ac
t
d
ata
to
d
ed
u
ce
k
n
o
wle
d
g
e
[
1
]
.
I
t
also
p
r
o
v
id
es
th
e
r
esea
r
ch
er
with
th
e
ab
ilit
y
to
im
p
r
o
v
e
k
n
o
wled
g
e
o
v
er
tim
e
an
d
with
ex
p
er
ien
ce
,
with
t
h
e
o
b
jectiv
e
o
f
d
is
co
v
e
r
in
g
h
id
d
e
n
p
atter
n
s
an
d
ex
p
lo
r
in
g
u
n
k
n
o
wn
d
ata.
T
h
er
ef
o
r
e,
ML
is
g
ain
in
g
m
o
r
e
atten
tio
n
in
ar
ea
s
in
v
o
lv
in
g
d
ata
an
aly
s
is
,
f
itti
n
g
,
d
ec
is
io
n
-
m
ak
in
g
,
an
d
au
to
m
at
io
n
.
Ma
ch
in
e
lear
n
in
g
is
ex
p
ec
ted
h
av
e
a
m
o
r
e
d
o
m
in
an
t
r
o
le
in
f
u
tu
r
e
e
m
er
g
in
g
telec
o
m
m
u
n
icatio
n
tech
n
o
lo
g
ies an
d
ar
ch
itectu
r
es
s
u
ch
as
in
in
ter
n
et
o
f
th
in
g
s
(
I
o
T
)
,
b
lo
c
k
ch
ain
,
an
d
5
G
n
etw
o
r
k
o
p
er
atio
n
s
an
d
m
an
ag
em
en
t
[
1
]
.
I
n
t
o
d
ay
’
s
co
m
p
lex
n
etw
o
r
k
ar
ch
itectu
r
e
an
d
em
er
g
in
g
d
em
a
n
d
s
f
o
r
v
ar
io
u
s
s
er
v
ices,
n
etwo
r
k
tr
af
f
ic
f
o
r
ec
ast
h
as
b
ec
o
m
e
in
c
r
ea
s
in
g
ly
v
ital
to
e
n
s
u
r
e
s
m
o
o
t
h
n
etwo
r
k
o
p
e
r
atio
n
s
an
d
m
an
ag
em
en
t.
Gen
e
r
ally
,
f
o
r
ec
asti
n
g
is
s
ee
n
as
a
tim
e
s
er
ies
d
ata
an
d
is
ac
co
r
d
in
g
ly
m
o
d
eled
v
ia
tim
e
s
er
ies
f
o
r
e
ca
s
t
tech
n
iq
u
es
to
estab
lis
h
a
co
r
r
elatio
n
b
etwe
e
n
p
r
ev
i
o
u
s
ly
o
b
s
er
v
ed
tr
af
f
ic
a
n
d
f
u
t
u
r
e
d
e
m
an
d
s
.
T
im
e
s
er
ies
an
aly
s
is
is
s
till
c
o
n
s
id
er
ed
a
c
h
allen
g
e
b
ec
au
s
e
it
in
v
o
lv
es
co
m
p
licated
co
m
b
in
atio
n
s
o
f
n
o
n
lin
ea
r
a
n
d
n
o
n
-
s
tatio
n
ar
y
d
y
n
am
ic
b
e
h
av
io
r
s
.
Statis
tically
,
d
y
n
am
ic
s
y
s
tem
s
p
r
o
d
u
c
e
a
n
o
n
-
lin
ea
r
tim
e
s
er
ies
if
th
e
o
u
tp
u
t
is
c
h
ar
ac
te
r
ized
b
y
n
o
n
-
lin
ea
r
f
ea
tu
r
es
s
u
ch
as
n
o
n
-
n
o
r
m
ality
,
ap
e
r
io
d
icity
,
an
d
n
o
n
lin
ea
r
ca
u
s
al
r
elatio
n
s
h
ip
s
b
etwe
en
l
ag
g
ed
v
ar
iab
les.
Gen
er
ally
,
two
b
r
o
ad
ap
p
r
o
a
ch
es
h
av
e
b
ee
n
u
s
ed
f
o
r
d
ev
elo
p
in
g
s
tatis
tical
an
aly
s
is
m
o
d
els
an
d
s
u
p
er
v
is
ed
ML
m
o
d
els.
Statis
tical
an
aly
s
is
m
o
d
els
ar
e
b
ased
o
n
th
e
g
en
er
alize
d
a
u
to
r
eg
r
ess
iv
e
in
teg
r
ated
m
o
v
in
g
av
e
r
ag
e
(
AR
I
M
A
)
m
o
d
el,
wh
ile
t
h
e
m
ajo
r
ity
o
f
tr
af
f
i
c
f
o
r
ec
asti
n
g
m
o
d
els
ar
e
b
ased
o
n
s
u
p
er
v
is
ed
ML
an
d
m
o
r
e
s
p
ec
if
ically
o
n
a
r
tifi
cial
n
eu
r
al
n
etwo
r
k
s
(
ANNs)
.
Ho
wev
er
,
AR
I
MA
-
b
ased
m
o
d
els
f
all
s
h
o
r
t
wh
en
d
ea
lin
g
with
n
o
n
lin
ea
r
a
n
d
n
o
n
-
s
tatio
n
ar
y
d
ata
[
1
]
,
[
2
]
.
T
h
e
m
ain
d
if
f
e
r
en
ce
b
etwe
en
n
eu
r
al
n
etwo
r
k
a
u
to
-
r
eg
r
ess
iv
e
(
NNAR
)
an
d
au
to
r
eg
r
ess
iv
e
in
teg
r
ated
m
o
v
i
n
g
av
er
ag
e
(
AR
I
MA
)
is
th
at
th
e
f
o
r
m
e
r
r
e
q
u
ir
es
a
s
tatio
n
ar
y
p
r
o
p
er
ty
t
o
b
e
im
p
o
s
ed
.
His
to
r
ically
,
d
if
f
er
en
t
t
y
p
es
o
f
ANNs
an
d
o
th
er
ML
tec
h
n
iq
u
es
h
a
v
e
b
ee
n
u
s
ed
f
o
r
f
o
r
ec
asti
n
g
t
h
e
tim
e
s
er
ies o
f
n
etwo
r
k
tr
af
f
ic.
Pre
p
r
o
ce
s
s
in
g
h
as
b
ec
o
m
e
cr
u
cial
in
d
ata
s
cien
ce
,
s
ig
n
al
p
r
o
ce
s
s
in
g
,
an
d
m
ac
h
i
n
e
lear
n
in
d
u
e
to
in
co
m
p
lete,
in
c
o
n
s
is
ten
t
(
co
n
tain
in
g
er
r
o
r
s
,
o
u
tlier
v
al
u
es),
an
d
v
a
r
y
in
g
n
o
is
e
p
atter
n
s
th
at
ex
is
t
an
d
ar
e
em
b
ed
d
e
d
in
co
llected
d
ata.
H
en
ce
,
p
r
ep
r
o
ce
s
s
in
g
m
eth
o
d
s
m
u
s
t b
e
em
p
lo
y
ed
b
ef
o
r
e
n
et
wo
r
k
f
o
r
ec
asti
n
g
ca
n
b
e
d
o
n
e
t
o
e
n
h
an
ce
d
ata
q
u
alit
y
.
I
n
tu
r
n
,
th
is
s
tep
will
en
h
an
ce
th
e
ac
c
u
r
ac
y
an
d
ef
f
icien
cy
o
f
n
o
n
-
lin
ea
r
au
to
r
eg
r
ess
iv
e
n
eu
r
al
n
etwo
r
k
(
NARNN
)
.
Pre
p
r
o
ce
s
s
in
g
tech
n
iq
u
es a
r
e
co
n
s
id
er
ed
cr
u
cial.
T
h
e
s
co
p
e
o
f
th
is
p
a
p
er
is
lim
itted
to
n
etwo
r
k
b
a
n
d
wid
th
f
o
r
ec
ast
an
d
n
o
t
t
h
e
g
e
n
er
al
p
r
o
b
l
em
o
f
tim
e
s
er
ies
f
o
r
ec
ast.
T
h
er
ef
o
r
e,
t
h
e
d
is
tin
ctiv
e
f
ea
tu
r
es
an
d
lim
itatio
n
s
o
f
n
o
ta
b
le
p
r
e
v
i
o
u
s
r
esear
ch
wer
e
s
u
m
m
ar
ized
.
T
h
e
d
ata
u
s
ed
w
as
co
llected
f
r
o
m
a
p
r
e
m
ier
in
ter
n
et
s
er
v
ic
e
p
r
o
v
id
er
r
e
p
r
esen
tin
g
an
lo
n
g
ter
m
ev
o
lu
tio
n
(
LTE
)
4
G
co
r
e
ag
g
r
eg
ated
b
an
d
wid
th
s
lice.
T
wo
f
o
r
ec
ast
tim
e
s
ca
les
wer
e
u
s
e
d
:
o
n
e
d
ay
an
d
o
n
e
wee
k
.
T
h
e
co
llected
d
ata
was
u
s
ed
to
d
ev
elo
p
a
f
o
r
ec
ast
m
o
d
e
l,
n
am
ely
a
u
n
iv
a
r
iate
tim
e
s
er
i
es
m
o
d
el.
A
h
y
b
r
id
nonl
in
ea
r
a
u
to
r
e
g
r
ess
iv
e
n
eu
r
al
n
etwo
r
k
was
u
s
ed
f
o
r
f
o
r
ec
asti
n
g
co
m
b
in
ed
with
v
ar
io
u
s
d
y
n
am
ic
s
m
o
o
th
in
g
tech
n
iq
u
es.
Sm
o
o
t
h
in
g
tech
n
i
q
u
es we
r
e
u
s
ed
to
e
n
h
an
ce
f
o
r
ec
ast ac
cu
r
ac
y
.
2.
RE
L
AT
E
D
WO
RK
C
o
r
tez
et
a
l.
[
3
]
u
s
ed
m
u
lti
lay
er
p
er
ce
p
tr
o
n
n
e
u
r
al
n
et
wo
r
k
(
MLP
-
NN
)
an
d
s
im
p
le
n
etwo
r
k
m
an
ag
em
en
t
p
r
o
to
c
o
l
(
SNMP
)
tr
af
f
ic
g
ath
er
e
d
f
r
o
m
two
d
i
f
f
er
en
t
in
ter
n
et
s
er
v
ice
p
r
o
v
id
e
r
(
I
SP
)
n
etwo
r
k
s
as
a
d
ataset.
T
wo
s
u
b
s
ets
wer
e
i
n
v
esti
g
ated
-
o
n
e
s
u
b
s
et
r
e
p
r
esen
tin
g
tr
a
f
f
ic
o
n
a
tr
an
s
-
Atlan
tic
lin
k
,
an
d
a
n
o
th
er
r
ep
r
esen
tin
g
ag
g
r
e
g
ated
t
r
af
f
i
c
in
th
e
b
ac
k
b
o
n
e
o
f
th
e
I
SP
.
Miss
in
g
SNMP
was
co
m
p
leted
u
s
in
g
lin
ea
r
in
ter
p
o
latio
n
.
T
h
e
p
er
f
o
r
m
a
n
c
e
o
f
th
e
p
r
o
p
o
s
ed
m
o
d
el
was
co
m
p
ar
ed
to
tr
ad
itio
n
al
Ho
lt
-
W
in
ter
s
m
o
d
els,
an
d
d
o
u
b
le
Ho
lt
-
W
in
ter
s
AR
I
MA
m
o
d
els.
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
NN
m
o
d
el
o
u
tp
e
r
f
o
r
m
ed
tr
ad
itio
n
al
AR
MA
m
o
d
els.
Ho
wev
er
,
t
h
e
p
r
o
p
o
s
e
d
m
o
d
el
was static a
n
d
d
i
d
n
o
t
r
ea
ct
to
th
e
d
y
n
am
ic
n
atu
r
e
o
f
tr
af
f
ic
lo
ad
s
.
C
h
ab
aa
et
a
l.
[
4
]
ev
alu
ate
d
v
ar
i
o
u
s
b
ac
k
p
r
o
p
ag
atio
n
(
BP
)
tr
ain
in
g
alg
o
r
ith
m
s
ML
P
-
NN
f
o
r
a
n
I
n
ter
n
et
tr
af
f
ic
tim
e
s
er
ies.
T
h
e
p
r
o
p
o
s
ed
wo
r
k
s
h
o
wed
th
at
L
e
v
en
b
e
r
g
-
Ma
r
q
u
a
r
d
t
(
L
M)
an
d
r
esil
ien
t
p
r
o
p
ag
atio
n
(
R
p
)
alg
o
r
ith
m
s
o
u
t
p
er
f
o
r
m
ed
o
th
e
r
B
P
alg
o
r
ith
m
s
.
Z
h
u
et
a
l.
[
5
]
,
a
h
y
b
r
id
t
r
ain
in
g
alg
o
r
ith
m
was
p
r
o
p
o
s
ed
b
ased
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
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6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
:
1
7
0
8
-
1
0
8
9
1080
o
n
an
a
r
tific
ial
b
ee
c
o
l
o
n
y
(
AB
C
)
alg
o
r
ith
m
th
at
e
m
p
lo
y
e
d
p
a
r
ticle
s
war
m
o
p
tim
izatio
n
(
PS
O)
,
an
ev
o
lu
tio
n
a
r
y
s
ea
r
ch
alg
o
r
ith
m
.
Mo
r
eo
v
e
r
,
a
(
5
;1
1
;1
)
ML
P
-
NN
was
u
s
ed
a
s
th
e
t
r
ain
in
g
alg
o
r
ith
m
.
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
p
r
o
p
o
s
ed
m
o
d
el
h
a
d
a
h
ig
h
er
p
r
e
d
ictio
n
ac
cu
r
ac
y
th
a
n
B
P.
Li
et
a
l.
[
6
]
u
s
ed
a
f
ee
d
f
o
r
wa
r
d
n
eu
r
al
n
etwo
r
k
to
p
r
ed
ict
i
n
co
m
in
g
a
n
d
o
u
tg
o
in
g
tr
af
f
ic
f
lo
ws.
T
h
e
s
tu
d
y
ar
g
u
ed
th
at
i
n
ter
-
d
ata
ce
n
ter
lin
k
is
d
o
m
in
ated
b
y
elep
h
an
t
f
lo
ws.
T
h
e
s
tu
d
y
u
s
ed
a
g
r
ad
ien
t
d
ec
en
t
an
d
a
wav
elet
tr
an
s
f
o
r
m
to
tr
ain
a
h
y
b
r
id
m
o
d
el.
SNMP
co
u
n
ter
s
an
d
to
tal
in
co
m
in
g
an
d
o
u
tg
o
i
n
g
d
ata
tr
af
f
ic
wer
e
g
ath
er
ed
in
3
0
-
s
ec
o
n
d
in
te
r
v
al
s
.
T
h
ese
d
ata
wer
e
u
s
ed
as th
e
d
ataset.
T
h
e
d
ata
we
r
e
c
o
llected
f
r
o
m
d
ata
ce
n
ter
(
DC
)
r
o
u
ter
s
f
o
r
a
p
e
r
io
d
o
f
s
ix
wee
k
s
.
T
h
e
tim
e
s
er
ies
was
d
ec
o
m
p
o
s
ed
u
s
in
g
a
lev
el
-
1
0
wav
elet
tr
an
s
f
o
r
m
.
Ho
wev
er
,
it
m
u
s
t
b
e
n
o
ted
th
at
th
e
wav
elet
tr
an
s
f
o
r
m
ca
n
ag
g
r
ess
iv
ely
elim
in
ate
p
ar
ts
o
f
th
e
o
r
ig
in
al
d
ata
if
n
o
t im
p
le
m
en
te
d
ca
r
ef
u
lly
.
Dy
ll
o
n
et
a
l.
[
7
]
d
e
v
elo
p
ed
a
n
o
n
lin
ea
r
au
to
r
e
g
r
ess
iv
e
ex
o
g
e
n
o
u
s
n
eu
r
al
(
NARX)
n
etwo
r
k
m
o
d
el
f
o
r
tim
e
s
er
ies
n
etwo
r
k
tr
af
f
ic
an
a
ly
s
is
.
T
h
e
s
tu
d
y
im
p
lem
en
te
d
a
n
eu
r
al
n
etwo
r
k
m
o
d
el
to
p
r
e
d
ict
th
e
f
u
tu
r
e
tr
en
d
s
o
f
th
e
L
o
n
d
o
n
So
u
th
B
an
k
Un
iv
er
s
ity
(
L
SB
U)
b
an
d
wid
th
d
a
ta
tr
af
f
ic.
Data
s
et
was
co
llected
u
s
in
g
t
h
e
p
ae
s
s
ler
r
o
u
ter
tr
af
f
ic
g
r
ap
h
er
(
PR
T
G)
to
o
l.
T
h
e
r
esu
lts
s
h
o
wed
th
at
NARX
n
eu
r
al
n
etwo
r
k
is
a
g
o
o
d
m
eth
o
d
f
o
r
p
r
ed
ictin
g
tim
e
s
er
ies d
ata.
Yo
o
an
d
Sim
[
8
]
p
r
o
p
o
s
ed
a
f
o
r
ec
ast
m
o
d
el
an
d
claim
e
d
it
co
u
ld
im
p
r
o
v
e
r
eso
u
r
ce
u
tili
za
tio
n
ef
f
icien
cy
in
h
ig
h
-
b
an
d
wid
t
h
n
etwo
r
k
s
to
ac
co
m
m
o
d
ate
t
h
e
r
is
e
in
d
ata
v
o
l
u
m
e
d
em
a
n
d
s
f
o
r
s
cien
tific
d
ata
ap
p
licatio
n
s
.
A
s
ea
s
o
n
al
d
ec
o
m
p
o
s
itio
n
o
f
tim
e
s
er
ies
b
y
L
OE
SS
(
STL
)
a
n
d
AR
I
MA
ar
e
u
s
ed
o
n
SNMP.
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
p
r
o
p
o
s
ed
f
o
r
ec
ast
m
o
d
el
was
r
esil
ie
n
t
ag
ain
s
t
ab
r
u
p
t
ch
a
n
g
es
in
n
etwo
r
k
u
s
ag
e.
T
h
e
m
u
ltis
tep
f
o
r
ec
ast wa
s
test
ed
as we
ll.
Af
o
lab
i
et
a
l.
[
9
]
d
is
cu
s
s
ed
th
e
s
ig
n
if
ican
ce
o
f
th
e
i
n
ter
f
er
e
n
ce
-
less
m
ac
h
in
e
lea
r
n
in
g
ap
p
r
o
ac
h
i
n
a
tim
e
s
er
ies
f
o
r
ec
ast
as
a
cr
u
cia
l
co
m
p
o
n
en
t
o
f
p
r
e
d
ictio
n
p
er
f
o
r
m
an
ce
,
esp
ec
ially
wh
e
n
f
o
r
e
ca
s
tin
g
m
an
y
s
tep
s
ah
ea
d
o
f
th
e
cu
r
r
e
n
tly
av
ailab
le
d
ata.
T
h
e
au
th
o
r
s
u
s
ed
Hilb
er
t
Hu
an
g
tr
an
s
f
o
r
m
atio
n
(
HHT
)
as
th
e
n
o
is
e
elim
in
atio
n
tech
n
i
q
u
e.
T
h
e
s
im
u
latio
n
r
esu
lts
wer
e
c
o
m
p
ar
ed
with
co
n
v
en
tio
n
al
an
d
s
tate
-
of
-
th
e
-
ar
t
ap
p
r
o
ac
h
es.
J
o
o
et
a
l.
[
1
0
]
p
r
o
p
o
s
ed
a
p
r
ed
ictio
n
m
eth
o
d
b
ased
o
n
wav
elet
f
ilter
in
g
.
T
h
e
p
r
o
p
o
s
ed
f
r
am
ewo
r
k
an
aly
ze
d
t
h
e
tim
e
s
er
ies
in
b
o
t
h
th
e
tim
e
an
d
f
r
e
q
u
en
c
y
d
o
m
a
in
s
.
T
h
e
p
r
o
p
o
s
ed
a
p
p
r
o
a
ch
wa
s
ap
p
lied
to
v
ar
i
o
u
s
s
ce
n
ar
io
s
.
T
h
e
r
esu
lts
s
h
o
wed
th
at
th
e
p
r
o
p
o
s
ed
m
eth
o
d
o
u
tp
er
f
o
r
m
ed
o
th
e
r
ap
p
r
o
ac
h
es
th
at
d
id
n
o
t
u
s
e
wav
elet
-
f
ilter
in
g
tech
n
iq
u
es.
B
.
Do
u
co
u
r
e
et
a
l.
[
1
1
]
in
tr
o
d
u
ce
d
a
p
r
e
d
ictio
n
m
eth
o
d
f
o
r
r
en
ewa
b
le
en
er
g
y
s
o
u
r
ce
s
to
in
tellig
en
tly
m
an
a
g
e
r
en
ewa
b
le
en
er
g
y
.
T
h
e
au
th
o
r
s
u
s
ed
w
av
elet
d
ec
o
m
p
o
s
itio
n
an
d
a
r
tific
ial
n
eu
r
al
n
etwo
r
k
s
an
d
d
is
cu
s
s
ed
th
e
s
ig
n
if
ican
ce
o
f
th
eir
r
esu
lts
.
Alawe
et
a
l.
[
1
2
]
p
r
o
p
o
s
ed
a
n
o
v
el
m
ec
h
a
n
is
m
to
s
ca
le
5
G
co
r
e
n
etwo
r
k
r
eso
u
r
ce
s
b
y
f
o
r
ec
ast
in
g
tr
af
f
ic
v
ia
ML
tech
n
iq
u
es.
T
h
e
p
r
ed
ictio
n
tech
n
iq
u
e
u
s
ed
was
b
ased
o
n
r
ec
u
r
r
e
n
t
n
eu
r
al
n
et
wo
r
k
s
(
R
NN
)
,
l
o
n
g
s
h
o
r
t
-
ter
m
m
em
o
r
y
(
L
STM
)
,
ar
tific
ial
n
eu
r
al
n
etwo
r
k
s
(
ANN
)
,
an
d
th
e
d
ee
p
n
eu
r
al
n
etwo
r
k
(
DNN)
.
C
o
m
p
ar
is
o
n
s
wer
e
m
ad
e
b
et
wee
n
th
e
d
if
f
er
e
n
t
tech
n
iq
u
e
s
.
T
h
e
s
im
u
latio
n
r
esu
lts
co
n
f
ir
m
ed
th
e
h
ig
h
er
ef
f
icien
cy
o
f
th
e
R
NN
-
b
ased
s
o
lu
tio
n
co
m
p
ar
e
d
to
th
e
o
th
er
a
p
p
r
o
ac
h
es.
No
p
r
ep
r
o
ce
s
s
in
g
o
r
f
ea
tu
r
e
e
x
tr
ac
tio
n
was m
ad
e
.
W
an
g
et
a
l.
[
1
3
]
p
r
o
p
o
s
ed
a
wav
elet
-
b
ased
n
e
u
r
al
n
etwo
r
k
m
o
d
el
,
ca
lled
th
e
m
u
ltil
ev
el
wav
elet
d
ec
o
m
p
o
s
itio
n
n
etwo
r
k
(
m
W
DN)
.
T
h
e
p
r
o
p
o
s
ed
m
o
d
el
u
s
e
d
th
e
wav
elet
d
ec
o
m
p
o
s
itio
n
i
n
f
r
eq
u
en
cy
lear
n
in
g
wh
ile
en
ab
lin
g
th
e
f
in
e
-
tu
n
in
g
o
f
all
p
ar
am
eter
s
u
n
d
er
a
d
ee
p
n
eu
r
al
n
etwo
r
k
f
r
a
m
ewo
r
k
.
T
h
e
r
esu
lts
s
h
o
wed
th
e
ef
f
ec
tiv
en
ess
o
f
th
e
p
r
o
p
o
s
ed
h
y
b
r
id
ap
p
r
o
ac
h
.
T
h
e
wav
el
et
d
ec
o
m
p
o
s
itio
n
r
e
q
u
ir
ed
s
ev
er
al
p
ar
am
eter
s
th
at
co
u
ld
a
f
f
ec
t
t
h
e
f
o
r
ec
ast
p
e
r
f
o
r
m
an
ce
s
u
ch
as
th
e
n
u
m
b
er
o
f
d
ec
o
m
p
o
s
itio
n
lev
els
a
n
d
th
e
s
elec
ted
m
o
th
er
wav
elet.
Salih
[
1
4
]
i
n
tr
o
d
u
ce
d
L
AN
o
f
f
ice
n
etwo
r
k
b
an
d
wid
th
p
r
ed
i
ctio
n
m
o
d
els
as
tim
e
s
er
ie
s
m
o
d
els.
T
h
e
p
r
o
p
o
s
ed
f
o
r
ec
ast
m
o
d
els
wer
e
test
ed
u
s
in
g
m
ea
n
s
q
u
ar
e
er
r
o
r
(
MSE
)
an
d
p
er
f
o
r
m
an
c
e
ev
alu
atio
n
p
lo
ts
.
Ho
wev
er
,
th
e
s
tu
d
y
d
id
n
o
t
u
s
e
an
y
p
r
e
p
r
o
ce
s
s
in
g
tech
n
i
q
u
es
.
J
.
Fen
g
et
a
l.
[
1
5
]
p
r
o
p
o
s
ed
a
d
ee
p
tr
a
f
f
ic
p
r
ed
icto
r
(
Dee
p
T
P)
m
o
d
el
to
f
o
r
ec
ast
lo
n
g
-
p
er
io
d
ce
llu
lar
n
etwo
r
k
tr
af
f
ic
.
T
h
e
s
tu
d
y
s
h
o
wed
th
at
th
e
m
o
d
el
o
u
tp
er
f
o
r
m
ed
o
th
er
t
r
af
f
ic
f
o
r
ec
ast
m
o
d
els
b
y
m
o
r
e
th
a
n
1
2
.
3
%.
Ho
wev
er
,
L
STM
is
n
o
t
s
u
itab
le
f
o
r
lo
n
g
-
p
e
r
io
d
f
o
r
ec
asti
n
g
(
m
u
lti
-
s
tep
s
ah
ea
d
)
.
Le
et
a
l.
[
1
6
]
p
r
o
p
o
s
ed
a
tr
af
f
ic
f
o
r
ec
asti
n
g
m
o
d
el
u
s
in
g
au
t
o
r
eg
r
ess
iv
e
m
o
d
els
an
d
n
eu
r
al
n
etwo
r
k
,
m
o
d
els
to
p
r
ed
ict
k
ey
p
er
f
o
r
m
a
n
ce
in
d
icato
r
s
(
KPI
s
)
in
n
etwo
r
k
KPI
f
o
r
lo
n
g
ter
m
an
d
s
h
o
r
t
-
ter
m
f
o
r
ec
asti
n
g
r
ea
l
d
ata.
Ho
wev
er
,
n
o
p
r
ep
r
o
ce
s
s
in
g
was
ap
p
lied
an
d
th
e
s
tu
d
y
o
n
ly
f
o
cu
s
ed
o
n
in
v
esti
g
atin
g
r
elatio
n
s
h
ip
s
b
et
wee
n
n
etwo
r
k
KPI
s
.
Yo
u
et
a
l
.
[
17
]
p
r
o
p
o
s
ed
a
h
y
b
r
id
L
OE
SS
-
AR
I
MA
-
b
ased
f
o
r
ec
ast
m
o
d
el.
Au
th
o
r
s
claim
e
d
th
at
s
u
c
h
a
m
o
d
el
h
as
th
e
p
o
ten
tial
o
f
en
h
an
cin
g
th
e
e
f
f
icien
cy
o
f
r
eso
u
r
ce
u
tili
za
tio
n
,
esp
ec
ially
i
n
h
i
g
h
-
s
p
ee
d
n
etwo
r
k
s
,
to
ac
co
m
m
o
d
ate
th
e
r
ap
id
in
cr
ea
s
e
in
r
is
in
g
d
em
an
d
s
f
o
r
s
cie
n
tific
d
ata
ap
p
licatio
n
s
.
A
s
ea
s
o
n
al
d
ec
o
m
p
o
s
itio
n
o
f
tim
e
s
er
ies
b
y
L
OE
SS
(
STL
)
an
d
(
AR
I
MA
)
was
ap
p
lied
o
n
s
im
p
le
n
etwo
r
k
m
a
n
ag
em
e
n
t
p
r
o
to
co
l
(
SNMP)
.
T
h
e
r
esu
lts
r
ev
ea
led
th
at
th
e
p
r
o
p
o
s
ed
f
o
r
ec
ast
m
o
d
el
was
r
esil
ien
t
ag
ain
s
t
ab
r
u
p
t
ch
an
g
es
in
n
etwo
r
k
u
s
ag
e
p
r
o
v
id
e
d
th
at
th
e
m
u
ltis
tep
f
o
r
ec
ast wa
s
u
s
ed
as th
e
p
r
im
ar
y
s
ce
n
ar
io
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
n
a
lysi
s
o
f h
yb
r
id
n
o
n
-
lin
ea
r
a
u
to
r
eg
r
ess
ive
n
eu
r
a
l n
etw
o
r
k
a
n
d
… (
Mo
h
a
med
K
h
a
l
a
fa
lla
Ha
s
s
a
n
)
1081
3.
RE
S
E
ARCH
M
E
T
H
O
D
T
h
e
ML
ap
p
r
o
ac
h
es
wer
e
m
o
d
eled
as
tim
e
s
er
ies
b
atch
lea
r
n
in
g
.
T
h
e
g
en
e
r
al
p
r
o
ce
s
s
o
f
n
etwo
r
k
b
an
d
wid
th
f
o
r
ec
ast
is
b
ased
o
n
m
ac
h
in
e
lea
r
n
in
g
.
T
h
is
alg
o
r
ith
m
was
ex
ten
d
ed
in
th
is
s
tu
d
y
b
y
p
r
e
p
r
o
ce
s
s
in
g
th
e
p
r
o
v
id
ed
d
ataset,
n
am
ely
b
y
elim
in
atin
g
u
n
n
ec
ess
ar
y
n
o
is
e
an
d
r
ap
id
tr
af
f
i
c
f
lu
ctu
at
io
n
s
.
Mo
r
e
o
v
er
,
to
av
o
id
th
e
er
o
s
io
n
o
f
p
e
r
io
d
ic
tr
en
d
s
an
d
p
atter
n
s
with
in
th
e
s
er
ies,
th
e
s
y
s
tem
lear
n
s
lo
ca
l
an
d
g
lo
b
al
tr
en
d
s
s
ep
ar
ately
to
d
etec
t
a
n
d
elim
in
ate
s
h
o
r
t
-
ter
m
o
r
lo
n
g
-
ter
m
n
o
is
e.
Similar
ap
p
r
o
ac
h
es
h
av
e
a
ls
o
b
ee
n
u
s
ed
in
t
h
e
p
ast
[7
]
-
[
1
1
]
,
with
th
e
v
a
r
io
u
s
tech
n
iq
u
es
u
s
ed
in
clu
d
i
n
g
Hi
lb
er
t
Hu
an
g
tr
a
n
s
f
o
r
m
atio
n
(
HHT
)
,
STL
,
an
d
th
e
wav
elet
-
b
ased
ap
p
r
o
ac
h
.
Ho
w
ev
er
,
it
is
o
f
ten
u
s
ed
t
o
d
etec
t
h
ig
h
n
o
is
e
lev
els
in
th
e
l
o
n
g
te
r
m
an
d
m
a
y
n
o
t b
e
s
u
itab
le
f
o
r
o
n
lin
e
o
r
s
em
i
-
o
n
lin
e
p
r
o
ce
s
s
e
s
,
wh
ile
th
e
c
u
r
r
en
t
s
tu
d
y
p
r
o
p
o
s
es
a
h
y
b
r
i
d
ap
p
r
o
ac
h
u
s
in
g
a
n
o
n
lin
ea
r
au
to
ag
g
r
ess
iv
e
n
eu
r
al
n
etwo
r
k
th
at
f
o
cu
s
es
m
ain
ly
o
n
lo
ca
l
v
a
r
iatio
n
s
u
s
in
g
v
ar
io
u
s
lo
ca
l
r
eg
r
ess
io
n
tech
n
iq
u
es
to
r
em
o
v
e
u
n
n
ec
ess
ar
y
n
o
is
e
an
d
f
lu
ct
u
atio
n
s
,
w
h
ich
m
ay
h
as
n
e
g
ativ
e
ef
f
ec
ts
o
n
th
e
p
r
e
d
ictio
n
ac
cu
r
ac
y
,
esp
ec
ially
i
n
n
o
n
lin
e
ar
an
d
n
o
n
-
s
tatio
n
ar
y
tim
e
s
er
i
es.
L
o
ca
l
r
eg
r
ess
io
n
a
p
p
r
o
ac
h
e
s
allo
w
th
e
r
em
o
v
al
o
f
n
o
is
e
an
d
f
lu
ctu
atio
n
s
in
s
h
o
r
t
s
ca
les
an
d
r
ea
ct
m
o
r
e
d
y
n
a
m
ically
to
n
o
is
e
-
lev
el
s
h
o
r
t
-
te
r
m
v
ar
iatio
n
s
m
o
r
e
th
an
o
t
h
e
r
wav
elet
-
a
n
d
HHT
-
b
ased
tech
n
i
q
u
es.
Similar
ap
p
r
o
ac
h
es
wer
e
also
u
tili
ze
d
in
o
n
e
s
tu
d
y
[
8
]
,
wh
ich
u
s
ed
AR
I
MA
in
s
tead
o
f
NAR.
T
h
e
ef
f
ec
ti
v
en
ess
o
f
th
e
p
r
o
p
o
s
ed
m
eth
o
d
was
v
e
r
if
ied
u
s
in
g
av
ailab
le
r
ea
l
n
etwo
r
k
tr
af
f
ic
d
atasets
.
3
.
1
.
Neura
l net
wo
r
k
a
ut
o
-
re
g
re
s
s
iv
e
(
NNAR
)
Neu
r
al
n
etwo
r
k
tr
ain
in
g
atte
m
p
ts
to
ap
p
r
o
x
im
ate
a
f
u
n
cti
o
n
b
y
o
p
tim
izin
g
n
etwo
r
k
weig
h
ts
an
d
n
eu
r
o
n
b
ias.
(
)
=
(
(
−
1
)
,
…
.
,
(
−
)
)
+
(
1
)
I
n
(
1
)
,
th
e
ter
m
ε
s
tan
d
s
f
o
r
er
r
o
r
.
T
h
e
y
in
p
u
t
f
ea
tu
r
es
(
B
an
d
wid
th
s
lice
in
th
i
s
ca
s
e)
(
−
1
)
,
(
−
2
)
,
(
−
3
)
ar
e
th
e
f
ee
d
b
ac
k
d
elay
s
.
T
r
ial
-
an
d
-
er
r
o
r
was
d
o
n
e
t
o
o
p
tim
iz
e
th
e
h
id
d
en
la
y
er
s
an
d
n
e
u
r
o
n
s
to
ac
h
iev
e
th
e
b
est
p
er
f
o
r
m
an
ce
.
Ho
wev
er
,
as
th
e
n
u
m
b
er
o
f
n
eu
r
o
n
s
i
n
cr
ea
s
es
as
th
e
s
y
s
te
m
b
ec
o
m
es
m
o
r
e
co
m
p
lex
,
th
e
lo
w
n
u
m
b
er
o
f
n
eu
r
o
n
s
m
ay
r
ed
u
ce
n
etwo
r
k
ef
f
icien
cy
.
L
ev
e
n
b
er
g
-
Ma
r
q
u
ar
d
t
is
th
e
m
o
s
t
wid
ely
u
s
ed
lear
n
in
g
r
u
le
d
u
e
to
its
f
ast
r
esp
o
n
s
e
[
9
]
.
T
h
e
r
o
o
t
m
ea
n
s
q
u
ar
ed
er
r
o
r
(
R
MSE
)
,
m
ea
n
s
q
u
ar
ed
er
r
o
r
(
MSE
)
,
an
d
th
e
er
r
o
r
s
u
m
o
f
s
q
u
a
r
es
(
SS
E
)
.
I
n
(
2
)
,
(
3
)
,
an
d
(
4
)
,
ar
e
o
f
ten
u
s
ed
as
th
e
p
er
f
o
r
m
an
ce
m
atr
ix
,
wh
er
e
y
i
̂
is
th
e
p
r
e
d
icted
d
ata,
is
th
e
cu
r
r
e
n
t d
ata,
an
d
is
th
e
n
u
m
b
er
o
f
d
ata
s
am
p
les [
9
]
.
I
n
th
is
r
esear
ch
,
th
e
g
r
ad
ien
t
d
escen
t
was
u
s
ed
as
th
e
lear
n
in
g
r
u
le.
NARNN
was
c
h
o
s
en
b
ec
au
s
e
L
STM
an
d
d
ee
p
l
ea
r
n
in
g
ap
p
r
o
ac
h
es
r
eq
u
ir
e
a
c
o
m
p
licated
an
d
ca
r
ef
u
l
d
esig
n
to
p
r
o
d
u
ce
ac
cu
r
a
te
f
o
r
ec
asts
.
I
n
ad
d
itio
n
to
th
a
t,
th
ese
tech
n
iq
u
es
wo
r
k
b
etter
with
h
ig
h
d
im
en
s
i
o
n
al
an
d
lar
g
e
d
atasets
.
T
h
er
e
f
o
r
e,
NARNN
was
s
elec
ted
in
th
is
r
esear
ch
as
th
e
f
o
r
ec
asti
n
g
tech
n
i
q
u
e.
=
∑
(
̂
−
)
2
=
1
(
2
)
=
(
3
)
R
MSE
=
√
1
∑
(
0
−
)
2
=
1
(
4
)
MA
E
=
∑
|
0
−
|
=
1
(
5
)
0
=
o
b
s
er
v
ed
=
Pre
d
icted
The
co
llected
d
ata
was
d
iv
id
ed
in
to
tr
ain
in
g
d
ata
an
d
test
in
g
d
ata.
T
h
e
tr
ain
in
g
s
tag
e
was
u
s
ed
to
test
th
e
m
o
d
el
f
it.
T
h
en
,
th
e
tim
e
s
er
ies
f
o
r
e
ca
s
tin
g
m
o
d
el
was
estab
lis
h
ed
u
s
in
g
th
e
tr
ain
e
d
m
o
d
el.
T
h
e
p
er
f
o
r
m
an
ce
was
m
ea
s
u
r
ed
ac
co
r
d
in
g
ly
an
d
t
h
e
n
co
m
p
a
r
ed
with
ac
tu
al
v
alu
es.
3
.
2
.
L
o
ca
l s
m
o
o
t
hin
g
t
ec
hn
i
qu
es
As d
is
cu
s
s
ed
in
s
ec
t
io
n
1
t
h
e
p
er
s
is
ten
ce
o
f
n
o
is
e
in
a
tim
e
s
er
ies f
o
r
ec
ast ca
n
h
av
e
co
n
tin
u
o
u
s
ly
an
d
cu
m
u
lativ
ely
im
p
air
f
o
r
ec
asti
n
g
p
er
f
o
r
m
an
ce
in
n
-
s
tep
s
ah
ea
d
f
o
r
ec
asts
,
s
o
th
is
is
s
u
e
h
as
to
b
e
tac
k
led
ca
r
ef
u
lly
wh
en
wo
r
k
in
g
with
f
o
r
ec
asti
n
g
alg
o
r
ith
m
s
wh
ile
m
in
im
izin
g
th
e
ef
f
ec
ts
o
f
h
ig
h
o
r
lo
w
f
r
e
q
u
en
cy
n
o
is
e
with
in
th
e
d
ata,
wh
ich
ca
n
b
e
u
s
ef
u
l
f
o
r
f
o
r
ec
asti
n
g
in
th
e
s
h
o
r
t
-
o
r
l
o
n
g
-
te
r
m
s
ca
le.
T
h
e
s
ig
n
if
ican
ce
o
f
n
o
is
e
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
:
1
7
0
8
-
1
0
8
9
1082
p
r
o
ce
s
s
in
g
o
r
r
em
o
v
al
was
a
d
d
r
ess
ed
in
p
ast
wo
r
k
[
7
]
-
[
1
1
]
.
Nex
t
Sectio
n
d
is
cu
s
s
es
v
ar
io
u
s
lo
ca
l
s
m
o
o
th
in
g
tech
n
iq
u
es u
s
ed
in
th
is
p
ap
er
.
3
.
2
.
1
.
L
o
ca
l r
eg
re
s
s
io
n t
ec
hn
iqu
e
s
T
h
e
lo
ca
l
r
eg
r
ess
io
n
m
eth
o
d
is
b
ased
o
n
t
h
e
L
OE
SS
m
eth
o
d
[
1
8
]
.
I
t
is
b
ased
o
n
f
itti
n
g
s
im
p
le
m
o
d
els
to
lo
ca
lized
d
ata
s
u
b
s
ets
to
f
o
r
m
a
cu
r
v
e
th
at
ap
p
r
o
x
im
ates
th
e
o
r
ig
in
al
d
ata.
T
h
e
o
b
s
er
v
atio
n
s
(
,
)
ar
e
ass
ig
n
ed
n
eig
h
b
o
r
h
o
o
d
weig
h
ts
u
s
in
g
th
e
tr
icu
b
e
weig
h
t
f
u
n
ctio
n
s
h
o
wn
i
n
(
6
)
.
L
et
∆
(
)
=
|
−
|
b
e
t
h
e
d
is
tan
ce
f
r
o
m
to
,
an
d
let
∆
(
)
be
th
ese
d
is
tan
ce
s
in
th
e
s
m
alles
t
t
o
lar
g
est
o
r
d
er
.
T
h
en
,
th
e
n
eig
h
b
o
r
h
o
o
d
weig
h
t f
o
r
t
h
e
o
b
s
er
v
atio
n
,
is
d
ef
in
ed
b
y
th
e
f
u
n
ctio
n
(
)
:
(
)
=
(
∆
(
)
∆
(
)
)
(
6
)
f
o
r
s
u
ch
th
at
∆
(
)
<
∆
(
)
,
wh
er
e
q
is
th
e
b
an
d
wid
th
th
at
d
ef
in
es
th
e
n
u
m
b
er
o
f
o
b
s
er
v
atio
n
s
in
th
e
s
u
b
s
et
o
f
d
ata
lo
ca
lized
ar
o
u
n
d
x
.
I
n
th
e
p
r
o
p
o
s
ed
alg
o
r
ith
m
,
th
is
ap
p
r
o
ac
h
was
ap
p
lied
to
f
it
a
tr
en
d
to
th
e
last
k
o
b
s
er
v
atio
n
s
o
f
r
eso
u
r
ce
u
tili
za
tio
n
.
Acc
o
r
d
in
g
ly
,
a
n
ew
tr
en
d
li
n
e
̂
(
)
=
̂
+
̂
(
)
is
f
o
u
n
d
f
o
r
ea
ch
n
e
w
o
b
s
er
v
atio
n
.
T
h
is
tr
en
d
lin
e
is
u
s
ed
to
esti
m
ate
th
e
n
ex
t o
b
s
e
r
v
atio
n
̂
(
+
1
)
.
T
h
e
n
ew
o
b
s
er
v
atio
n
ca
n
b
e
in
th
e
f
o
r
m
o
f
h
o
s
t
r
eso
u
r
ce
u
tili
za
tio
n
s
u
ch
as
b
an
d
wid
t
h
s
lice
u
tili
za
tio
n
[
1
8
]
.
I
n
(
7
)
s
h
o
w
s
th
e
f
in
al
f
o
r
ec
ast
f
o
r
m
u
la
u
s
in
g
h
y
b
r
id
L
OE
SS
an
d
NARNN:
=
0
+
∑
=
1
+
(
∑
(
=
1
̂
(
+
1
)
)
−
1
+
0
)
+
(
7
)
wh
er
e
is
th
e
n
u
m
b
er
o
f
en
tr
ie
s
,
is
th
e
n
u
m
b
er
o
f
h
id
d
en
la
y
er
s
with
ac
tiv
atio
n
f
u
n
ctio
n
,
an
d
is
th
e
p
ar
am
eter
co
r
r
esp
o
n
d
in
g
to
th
e
weig
h
t
o
f
t
h
e
co
n
n
ec
tio
n
b
etwe
en
th
e
in
p
u
t
u
n
it
an
d
th
e
h
i
d
d
en
u
n
it
,
is
th
e
weig
h
t
o
f
th
e
co
n
n
ec
tio
n
b
etwe
en
th
e
h
i
d
d
en
u
n
it
a
n
d
th
e
o
u
tp
u
t
u
n
it,
an
d
0
an
d
0
ar
e
th
e
co
n
s
tan
ts
th
at
co
r
r
esp
o
n
d
,
r
esp
ec
tiv
ely
,
to
t
h
e
h
id
d
e
n
u
n
it
an
d
th
e
o
u
tp
u
t
u
n
it.T
wo
f
o
r
m
s
u
s
e
L
OW
E
SS
,
wh
ich
u
s
es
a
f
ir
s
t
-
d
eg
r
ee
p
o
ly
n
o
m
ial
m
o
d
e
l
with
weig
h
ted
lin
ea
r
least
s
q
u
ar
es
an
d
L
OE
SS
,
wh
ic
h
u
s
es
a
s
ec
o
n
d
-
d
eg
r
ee
p
o
ly
n
o
m
ial
m
o
d
el
[
1
8
]
.
3
.
2
.
2
.
Ro
bu
s
t
lo
ca
l r
eg
re
s
s
io
n
T
h
is
s
tu
d
y
ad
o
p
ted
t
h
e
L
R
m
eth
o
d
b
u
t
t
h
e
f
ir
s
t
f
it
was
ca
r
r
ied
o
u
t
with
weig
h
ts
d
ef
i
n
ed
u
s
in
g
th
e
tr
icu
b
e
weig
h
t
f
u
n
ctio
n
.
T
h
e
f
it
was
e
v
alu
ated
at
th
e
to
g
et
t
h
e
f
itted
v
al
u
es
(
̂
)
,
an
d
t
h
e
r
esid
u
als
̂
=
̂
−
,
at
ea
ch
o
b
s
er
v
atio
n
(
,
)
,
th
e
ad
d
itio
n
al
r
o
b
u
s
tn
ess
weig
h
t
was
ca
lcu
lated
,
s
u
b
jecte
d
to
a
m
ag
n
itu
d
e
o
f
̂
.
Acc
o
r
d
i
n
g
ly
,
a
n
ew
weig
h
t
(
)
was
ass
ig
n
ed
to
ea
ch
o
b
s
er
v
atio
n
,
wh
e
r
e
is
d
ef
in
ed
as
in
(
8
)
[
1
8
]
.
=
{
(
1
−
(
ε
̂
i
6
MA
D
)
2
)
2
,
|
ε
̂
i
|
<
6
MAD
0
,
|
ε
̂
i
|
≥
6
MAD
}
(
8
)
wh
er
e
MA
D
is
d
ef
in
ed
p
e
r
(
9
)
:
=
(
|
̂
|
)
(
9
)
Similar
ly
,
two
v
er
s
io
n
s
wer
e
e
x
am
in
ed
,
i.e
.
,
'
R
L
O
W
E
SS
'
an
d
'
R
L
OE
SS
'
.
I
n
b
o
th
f
o
r
m
s
,
th
e
l
o
wer
weig
h
ts
wer
e
ass
ig
n
ed
to
th
e
o
u
tlier
s
in
th
e
r
eg
r
es
s
io
n
.
M
o
r
eo
v
e
r
,
o
u
ts
id
e
th
e
s
ix
m
ea
n
ab
s
o
lu
te
d
ev
ia
tio
n
s
,
ze
r
o
weig
h
ts
wer
e
ass
ig
n
ed
to
n
ew
v
al
u
es.
3
.
2
.
3
.
M
o
v
ing
a
v
er
a
g
e
I
n
s
ev
er
al
d
o
m
ain
s
,
tim
e
s
er
ie
s
d
ata
is
u
s
u
ally
s
m
o
o
t
h
ed
u
s
in
g
m
o
v
in
g
av
er
a
g
es (
MA
s
)
.
T
h
is
m
eth
o
d
is
u
s
ed
esp
ec
ially
in
tr
en
d
f
o
r
e
ca
s
tin
g
.
T
h
e
m
o
v
i
n
g
av
er
ag
e
i
s
co
n
s
id
er
ed
a
ty
p
e
o
f
r
ea
l
-
tim
e
f
ilter
th
at
r
em
o
v
es
h
ig
h
f
r
eq
u
e
n
cies
f
r
o
m
d
ata.
I
n
s
ig
n
al
p
r
o
ce
s
s
in
g
,
MA
s
ar
e
th
er
ef
o
r
e
also
ca
lled
“lo
w
-
p
ass
f
ilter
s
”
[
1
9
]
wh
e
r
e
th
e
ca
lcu
lated
co
ef
f
icie
n
ts
ar
e
eq
u
al
to
th
e
r
ec
ip
r
o
ca
l
o
f
th
e
s
p
an
o
r
b
a
n
d
wid
th
.
Mo
v
in
g
av
er
ag
es
ar
e
also
k
n
o
wn
as
“e
x
p
o
n
en
tial
s
m
o
o
t
h
in
g
”.
L
et’
s
d
ef
in
e
as
th
r
o
u
g
h
p
u
t
at
th
e
tim
e
i.
L
et
=
{
}
,
=
1
…
.
.
b
e
th
e
tim
e
s
er
ies
wh
er
e
p
is
th
e
tim
e
s
er
ies
len
g
th
.
T
h
e
r
ef
o
r
e,
th
e
m
o
v
in
g
av
e
r
ag
e
o
f
th
e
p
er
io
d
q
at
tim
e
ca
n
b
e
ca
lcu
lated
as
p
er
(
1
0
)
[
1
9
]
.
In
(1
0
)
a
n
d
(
1
1
)
s
h
o
w
th
e
f
in
al
f
o
r
ec
ast
f
o
r
m
u
la
u
s
in
g
h
y
b
r
i
d
m
o
v
in
g
av
er
ag
e
an
d
NARNN:
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
n
a
lysi
s
o
f h
yb
r
id
n
o
n
-
lin
ea
r
a
u
to
r
eg
r
ess
ive
n
eu
r
a
l n
etw
o
r
k
a
n
d
… (
Mo
h
a
med
K
h
a
l
a
fa
lla
Ha
s
s
a
n
)
1083
=
1
∑
−
+
1
=
1
(
1
0
)
=
0
+
∑
=
1
+
(
∑
(
=
1
(
)
−
1
)
−
1
+
0
)
+
(
1
1
)
3
.
2
.
4
.
Sa
v
it
z
k
y
-
G
o
la
y
s
m
o
o
t
hin
g
f
ilte
r
T
h
e
Sav
itzk
y
-
Go
lay
(
SG)
s
m
o
o
th
in
g
f
ilter
is
co
n
s
id
er
ed
a
ty
p
e
o
f
lo
w
-
p
ass
f
ilter
ch
ar
ac
ter
ized
b
y
two
p
ar
am
eter
s
d
en
o
ted
as
K
a
n
d
M.
T
h
e
SG
f
ilter
ca
n
b
e
d
e
f
in
ed
as
a
weig
h
te
d
m
o
v
in
g
a
v
er
ag
e,
i.e
.
,
a
f
in
ite
im
p
u
ls
e
r
esp
o
n
s
e
(
FIR)
f
ilter
.
Fil
ter
co
ef
f
icien
t
s
ar
e
ca
lcu
lated
u
s
in
g
an
u
n
-
weig
h
ted
lin
ea
r
least
-
s
q
u
ar
es
r
eg
r
ess
io
n
an
d
a
p
o
l
y
n
o
m
ial
m
o
d
el
o
f
a
s
p
ec
if
ied
d
eg
r
ee
(
th
e
d
ef
au
lt
is
2
)
.
T
h
e
tim
e
s
er
ies
to
b
e
esti
m
ated
is
d
o
n
ated
b
y
x(
n
)
,
s
o
t
h
e
f
in
al
o
u
tp
u
t is o
b
tain
ed
u
s
in
g
(
1
2
)
,
(
1
3
):
̂
(
)
=
∑
ℎ
(
)
(
−
)
=
−
(
1
2
)
=
0
+
∑
=
1
+
(
∑
(
=
1
(
̂
(
)
)
−
1
)
−
1
+
0
)
+
(
1
3
)
No
te
th
at
a
h
ig
h
er
d
e
g
r
ee
p
o
ly
n
o
m
ial
m
ak
es
it
p
o
s
s
ib
le
to
ac
h
iev
e
a
h
ig
h
lev
el
o
f
s
m
o
o
t
h
in
g
with
o
u
t
atten
u
atin
g
th
e
d
ata
f
ea
t
u
r
es
[
2
0
]
.
I
t
is
wo
r
th
m
en
tio
n
in
g
th
at
L
OE
SS
is
u
s
ed
f
o
r
s
eas
o
n
al
d
e
co
m
p
o
s
itio
n
,
b
u
t
i
n
th
is
wo
r
k
,
th
e
f
o
cu
s
was
to
u
s
e
L
OE
SS
an
d
o
t
h
er
lo
cal
r
eg
r
ess
io
n
tech
n
i
q
u
es
as
s
m
o
o
t
h
en
i
n
g
tech
n
iq
u
es,
s
i
n
ce
d
eco
m
p
o
s
itio
n
m
ay
ag
g
r
ess
iv
el
y
r
em
o
v
e
s
o
m
e
o
f
th
e
im
p
o
r
tan
t
d
ataset
f
eatu
r
es.
No
w,
th
e
q
u
est
io
n
b
eco
m
es
h
o
w
t
o
s
elect
th
e
b
an
d
wid
t
h
q
.
T
h
e
b
an
d
wid
th
p
la
y
s
a
cr
itical
r
o
le
in
th
e
o
v
er
all
lo
cal
r
eg
r
ess
io
n
f
it;
if
th
e
b
an
d
wid
t
h
s
elected
is
v
er
y
s
m
all,
lar
g
e v
ar
ian
ces
wi
ll
r
esu
lt,
as
i
n
s
u
f
f
icien
t
d
ata will
f
all
with
in
th
e
s
m
o
o
th
i
n
g
wi
n
d
o
w,
an
d
,
as
a resu
lt
,
a
n
o
is
y
f
it
will
b
e
p
r
o
d
u
ced
.
O
n
th
e
o
t
h
er
h
an
d
,
if
it
is
v
er
y
l
ar
g
e,
n
o
t
all
d
ata
will
b
e
f
itted
with
in
th
e
s
p
ecif
ied
win
d
o
w.
I
d
eally
,
a
s
ep
ar
ate
b
an
d
wid
th
f
o
r
each
f
ittin
g
p
o
in
t
is
u
s
e
d
,
b
ear
in
g
i
n
m
in
d
f
eatu
r
es
s
u
ch
as
th
e
lo
c
al
d
en
s
it
y
.
Pra
ctically
,
it
is
d
if
f
icu
lt
to
s
elect
an
o
p
tim
u
m
q
v
al
u
e,
as
th
e
r
esear
ch
er
d
o
es
n
o
t
wan
t
t
o
u
n
in
ten
tio
n
ally
elim
in
ate
d
ata.
T
h
e
s
im
p
lest
ap
p
r
o
ach
is
to
s
elect
q
as
a
co
n
s
tan
t
f
o
r
all
.
T
h
is
case
co
u
l
d
b
e
s
atis
f
acto
r
y
f
o
r
s
o
m
e
s
im
p
le
co
n
s
t
an
t
v
ar
ian
ce
d
ata,
b
u
t
w
h
en
th
e
in
d
e
p
en
d
e
n
t
v
ar
iab
les
h
av
e
a
n
o
n
-
u
n
if
o
r
m
d
is
tr
ib
u
tio
n
s
u
ch
as
in
th
e
b
an
d
wid
t
h
s
lice,
p
r
o
b
lem
s
s
u
ch
as
em
p
ty
n
eig
h
b
o
r
h
o
o
d
s
an
d
t
h
e
accid
en
tal
r
em
o
v
al
o
f
m
o
r
e
u
n
n
ecess
ar
y
d
ata
co
u
ld
r
esu
lt.
T
h
er
ef
o
r
e,
th
e fo
llo
win
g
ap
p
r
o
ach
s
h
o
wn
in
Alg
o
r
ith
m
1
was
p
r
o
p
o
s
ed
:
Alg
o
r
ith
m
1
Input y as time series bandwidth utilization
Output MSE
y
̂
as a locally fitted (predicted) value using local smoothing techniques
1
—
Initialize, set q as 0
2
—
perform local smoothing using selected q
3
—
set q = q + 0.001
4
—
calculate the average MSE for all q
-
values
5
—
if MSE is = 0, then go to 2, else stop
6
—
set q
q
7
—
return
y
̂
Fig
u
r
e
1
s
h
o
ws
t
h
e
ef
f
ects
o
f
d
if
f
er
en
t
q
-
v
alu
es
an
d
t
h
eir
co
r
r
esp
o
n
d
in
g
d
if
f
er
en
c
es
f
r
o
m
th
e
o
r
ig
in
al
B
an
d
wid
t
h
u
tilizati
o
n
.
I
t
is
o
b
v
i
o
u
s
t
h
at
as
th
e
q
-
v
alu
e
i
n
cr
eases
,
th
e
s
m
o
o
th
er
t
h
e
cu
r
v
e,
b
u
t
t
h
e
d
if
f
er
en
ce
(
er
r
o
r
)
will
in
cr
ease,
in
tu
r
n
,
i
n
cr
easin
g
th
e
o
v
er
all
ab
s
o
lu
te
m
ean
s
q
u
ar
ed
er
r
o
r
(
MS
E
)
.
I
n
th
is
p
ap
er
,
N
NAR
(
p
,
k
)
was
u
s
ed
to
in
d
icate
p
lag
g
ed
i
n
p
u
t
s
an
d
k
n
o
d
es
i
n
th
e
h
i
d
d
en
la
y
er
.
T
h
e
g
en
er
al
ap
p
r
o
ach
to
s
ear
ch
in
g
f
o
r
th
e
o
p
tim
al
s
tr
u
ctu
r
e
f
o
r
th
e
NNAR
m
o
d
el
is
th
r
o
u
g
h
tr
ial
-
an
d
-
er
r
o
r
,
p
er
f
o
r
m
ed
b
y
test
in
g
n
u
m
er
o
u
s
n
etwo
r
k
s
wit
h
v
ar
y
in
g
n
u
m
b
er
s
o
f
in
p
u
ts
a
n
d
h
i
d
d
en
u
n
its
an
d
th
e
n
calcu
latin
g
th
e
g
e
n
er
alizatio
n
er
r
o
r
o
f
e
ach
to
ach
iev
e
a
s
tr
u
ctu
r
e
with
th
e
lo
west
g
en
er
alizatio
n
er
r
o
r
[
2
1
]
,
[
2
2
]
.
T
h
e
cr
u
cial
p
ar
t
o
f
NNAR
m
o
d
elin
g
is
t
o
f
in
d
t
h
e
ap
p
r
o
p
r
iat
e
v
alu
es
f
o
r
p
an
d
k
lag
g
ed
i
n
p
u
ts
.
I
n
th
is
wo
r
k
,
Ak
aik
e’
s
in
f
o
r
m
atio
n
cr
iter
io
n
(
AI
C
)
[
2
1
]
-
[
2
3
]
was
u
s
e
d
to
au
to
m
ate
th
e
p
ar
am
eter
s
electio
n
p
r
o
cess
u
s
i
n
g
R
p
r
o
g
r
am
m
in
g
lan
g
u
ag
e.
I
n
f
act,
th
i
s
m
eth
o
d
is
asy
m
p
to
t
ically
eq
u
i
v
alen
t
t
o
cr
o
s
s
-
v
alid
atio
n
[
2
3
]
.
T
h
e
b
est
m
o
d
el
with
p
an
d
k
was
t
h
en
ch
o
s
en
with
th
e
least
v
alu
e
o
f
AI
C
u
s
in
g
th
e
R
la
n
g
u
ag
e.
T
wo
s
cen
ar
io
s
wer
e
ex
am
in
e
d
in
t
h
is
p
ap
er
-
th
e
s
h
o
r
t
-
ter
m
f
o
r
ecast,
wh
ich
s
h
o
ws
h
o
w
each
h
y
b
r
id
tech
n
iq
u
e
will
p
er
f
o
r
m
o
n
th
e
s
h
o
r
t
-
ter
m
s
cale,
an
d
th
e
s
eco
n
d
s
cen
ar
io
,
wh
ich
s
h
o
ws
th
e
f
o
r
ecast
p
er
f
o
r
m
an
ce
o
n
a
lo
n
g
-
ter
m
s
cale
f
o
r
ecast.
E
ach
tim
e
s
tep
r
ep
r
esen
ts
2
8
.
8
m
in
u
t
es
an
d
e
v
er
y
5
0
tim
e
s
tep
s
r
ep
r
esen
t
o
n
e
d
ay
.
T
h
is
case
is
d
u
e
t
o
t
h
e
lim
itatio
n
s
i
n
th
e
d
ata
co
llectio
n
to
o
l.
T
h
e
v
alu
es
wer
e
th
e
n
i
n
ter
p
o
lated
,
r
esu
ltin
g
i
n
a
tim
e
s
er
ies
m
o
d
el.
T
h
e
m
u
lti
-
s
cale
f
o
r
ecast
was
u
s
ed
to
in
v
esti
g
ate
t
h
e
e
x
t
en
t
to
wh
ich
t
h
e
h
y
b
r
id
tech
n
i
q
u
es
wo
u
ld
p
er
f
o
r
m
b
etter
th
an
v
ar
io
u
s
f
o
r
ecast
win
d
o
ws.
T
h
e
f
in
d
i
n
g
will
p
r
o
v
e
b
en
ef
icial
f
o
r
r
eal
-
wo
r
ld
co
r
e
an
d
b
ack
b
o
n
e
n
etw
o
r
k
s
to
ach
iev
e
ef
f
icien
t
n
etwo
r
k
r
eso
u
r
ce
p
la
n
n
in
g
.
I
n
th
is
p
ap
er
,
t
o
en
h
an
ce
tim
e
s
er
ies
f
o
r
ecast
m
o
d
els,
th
e
B
o
x
a
n
d
C
o
x
[
2
4
]
p
o
wer
tr
an
s
f
o
r
m
atio
n
was
u
s
ed
to
n
o
r
m
alize
s
er
ies
v
ar
ian
ces.
Mo
r
eo
v
er
,
th
e
au
g
m
en
ted
Dick
y
-
Fu
ller
(
ADF)
test
[
2
4
]
was
u
s
ed
t
o
co
n
f
ir
m
th
e
s
tatio
n
ar
ity
o
f
th
e
tim
e
s
er
ies
alt
h
o
u
g
h
NARNN
can
b
e
u
s
ed
to
m
o
d
el
a
n
o
n
-
s
tatio
n
ar
y
tim
e
s
er
ies.
Pre
v
io
u
s
wo
r
k
h
ad
ad
v
is
ed
ex
am
in
i
n
g
t
h
e
s
tatio
n
ar
ity
o
f
r
eg
r
ess
io
n
m
o
d
els,
as
s
tati
o
n
ar
ity
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
:
1
7
0
8
-
1
0
8
9
1084
co
u
ld
lea
d
to
m
is
lead
in
g
r
esu
lts
[
2
5
]
.
T
o
m
easu
r
e th
e
s
tatio
n
ar
it
y
o
f
c
o
llected
d
atasets
,
ta
u
s
tati
s
ti
cs
was
u
s
e
d
.
F
o
r
a
T
y
p
e
I
test
,
th
e
ta
u
cr
itical
v
alu
e
is
−
2
.
9
8
5
wh
e
n
n
=
7
0
0
(
th
e
d
atasets
ar
e
co
m
p
o
s
ed
o
f
7
0
0
d
ata
p
o
in
t
s
)
.
Sin
ce
τ
crit
=
−
2
.
2
2
3
<
−
1
0
.
1
4
1
4
7
=
τ
,
th
e n
u
ll
h
y
p
o
t
h
esis
t
h
at t
h
e ti
m
e s
er
ies
is
n
o
t
s
tatio
n
ar
y
i
s
r
ejected
4.
RE
SU
L
T
S AN
D
D
I
SCU
S
S
I
O
N
Fig
u
r
e
1
(
a)
s
h
o
ws
th
e
L
T
E
b
an
d
wid
th
u
tilizatio
n
with
o
u
t
s
m
o
o
th
i
n
g
wh
ile
Fig
u
r
es
1
(
b
)
s
h
o
w
th
e
ef
f
ects
o
f
ap
p
ly
i
n
g
m
o
v
i
n
g
av
er
ag
e
s
m
o
o
th
in
g
tec
h
n
iq
u
es
u
s
in
g
q
=
0
.
0
0
2
wh
ile
Fig
u
r
e
1
(
c)
s
h
o
ws
t
h
e
ef
f
ects
o
f
ap
p
ly
in
g
m
o
v
in
g
av
er
ag
e
s
m
o
o
t
h
in
g
tech
n
iq
u
es
u
s
i
n
g
q
=
0
.
0
0
3
As
s
h
o
w
n
in
Fig
u
r
e
1
(
a)
,
it
is
o
b
v
io
u
s
th
at
th
e
b
an
d
wid
t
h
s
lic
e
ex
h
ib
ited
s
i
g
n
if
ican
t
s
easo
n
al
p
atter
n
s
with
d
aily
p
eak
s
.
Nev
er
th
eless
,
th
e
d
ata
also
s
h
o
ws
a
s
to
ch
asti
c
p
atter
n
b
etween
s
u
ccess
iv
e
p
o
in
t
s
with
co
n
tin
u
o
u
s
ir
r
eg
u
lar
f
lu
ctu
atio
n
s
.
On
th
e
o
t
h
er
h
an
d
,
n
o
l
o
n
g
-
ter
m
t
r
en
d
ap
p
ear
ed
to
ex
is
t.
Min
im
u
m
s
m
o
o
th
in
g
b
an
d
wid
th
(
q
)
was
s
elected
as
in
to
r
d
u
ced
i
n
s
ectio
n
2
in
alg
o
r
ith
m
1
.
Fro
m
Fig
u
r
e
1
(
b
)
,
it
is
n
o
tica
b
le
th
at
th
e
ef
f
ects
o
f
ap
p
ly
in
g
s
m
o
o
t
h
i
n
g
tech
n
iq
u
es
can
b
e
d
if
f
icu
lt
to
b
e
o
b
s
er
v
ed
b
y
t
h
e
n
ak
ed
ey
e.
T
h
er
ef
o
r
e,
MSE
was
acco
r
d
in
g
ly
calcu
lated
f
o
r
each
tech
n
i
q
u
e
as
d
ep
icted
in
T
ab
le
1
,
w
h
ich
s
h
o
ws
t
h
e
ef
f
ect
o
f
ap
p
ly
in
g
v
ar
io
u
s
s
m
o
o
t
h
in
g
tech
n
iq
u
es
o
n
th
e
s
elected
d
ataset.
Fig
u
r
e
1
(
b
)
s
h
o
ws
t
h
e
L
T
E
s
lice
b
an
d
wid
th
u
tilizatio
n
s
m
o
o
th
ed
with
t
h
e
m
o
v
in
g
av
er
ag
e
(
M
A)
an
d
s
m
o
o
t
h
in
g
win
d
o
w
q
=
0
.
0
0
3
,
wh
ic
h
r
em
o
v
es
m
o
r
e
o
f
th
e
s
m
all
f
lactu
atio
n
s
at
t
h
e
to
p
p
ea
k
s
,
t
h
u
s
p
r
o
d
u
cin
g
th
e
h
i
g
h
est
MSE
o
u
t
o
f
all
th
e
o
th
er
tech
n
i
q
u
es.
I
n
th
i
s
case,
(
q)
h
as
a
d
ir
ect
in
f
lu
en
ce
o
n
th
e
s
m
o
o
th
in
g
p
er
f
o
r
m
an
ce
s
in
ce
it
is
in
v
er
s
ly
p
r
o
p
o
tio
n
al
to
t
h
e
MSE
.
T
h
er
ef
o
r
e,
a
s
ig
n
if
ican
t
p
o
r
ti
o
n
o
f
th
e
d
ata
c
o
u
ld
b
e
r
em
o
v
ed
if
h
ig
h
er
(
q)
v
alu
es
wer
e
u
s
ed
.
I
n
f
act,
th
e
h
ig
h
er
th
e
(
q)
v
alu
es,
th
e
b
etter
th
e
s
m
o
o
th
i
n
g
an
d
th
e
la
r
g
er
am
o
u
n
t
o
f
d
ata
th
at
will
b
e
lo
s
t
as
d
e
p
icted
in
Fi
g
u
r
e
1
(
c)
.
C
o
n
ce
q
u
e
n
tly
,
i
n
to
d
ay
’
s
d
ata
-
cen
tr
ic
wo
r
ld
,
lo
s
i
n
g
ev
en
s
m
all
am
o
u
n
ts
o
f
d
ata
co
u
ld
lead
to
t
h
e
v
i
o
latio
n
o
f
s
er
v
i
ce
lev
el
ag
r
eem
en
ts
in
ad
d
iti
o
n
to
in
ef
f
icien
t
r
eso
u
r
ce
u
tilizatio
n
an
d
p
lan
n
in
g
.
T
h
e
r
ef
o
r
e,
(
q
)
h
as
to
b
e
s
elected
acco
r
d
in
g
t
o
alg
o
r
ith
m
(
1
)
.
LO
W
E
SS
p
r
o
d
u
ced
th
e
s
e
co
n
d
lar
g
est
MSE
,
as
s
h
o
wn
i
n
T
ab
le
1
,
d
u
e
to
t
h
e
lik
eli
h
o
o
d
th
at
th
e
n
o
n
li
n
ear
b
an
d
wid
t
h
s
lice
wo
u
l
d
less
lik
el
y
f
it
if
th
e
f
ir
s
t
-
d
eg
r
ee
p
o
ly
n
o
m
ial
lin
ear
m
o
d
el
was
u
s
ed
.
Ho
wev
er
,
f
ittin
g
u
s
i
n
g
th
e
q
u
ad
r
atic p
o
ly
n
o
m
ial
b
a
s
ed
o
n
L
OE
SS
p
r
o
d
u
ced
a s
m
aller
MSE
,
as
s
h
o
wn
in
T
ab
le
1
,
d
u
e
to
t
h
e n
o
n
li
n
ear
ity
o
f
th
e
s
eco
n
d
-
o
r
d
er
lo
cal
f
ittin
g
m
o
d
e
ls
,
as
s
h
o
wn
i
n
Fig
u
r
e
1
(
a
)
.
On
th
e
o
th
er
h
an
d
,
th
e
s
g
o
lay
f
ilter
p
r
o
d
u
ce
d
a
s
m
aller
MSE
u
s
in
g
a
s
eco
n
d
-
d
eg
r
ee
p
o
ly
n
o
m
ial,
in
c
o
n
tr
ast
to
L
OE
SS,
wh
ic
h
u
s
ed
a
s
eco
n
d
-
d
e
g
r
ee
p
o
ly
n
o
m
ial
in
wh
ich
th
e
weig
h
t
s
wer
e
s
tr
o
n
g
l
y
i
n
f
lu
e
n
ced
b
y
th
e
q
b
an
d
wid
th
,
as
s
h
o
wn
in
(
6
)
Fi
n
ally
,
R
L
OE
SS
an
d
R
L
OW
E
SS
s
h
ar
ed
a s
im
ilar
p
er
f
o
r
m
an
ce,
y
ield
in
g
th
e lo
west
MSE
v
alu
es,
as
s
h
o
w
n
in
T
ab
le
1
.
T
ab
le
1
.
T
h
e
ef
f
ec
ts
o
f
ap
p
ly
i
n
g
alg
o
r
ith
m
1
S
mo
o
t
h
i
n
g
Te
c
h
n
i
q
u
e
q
S
mo
o
t
h
i
n
g
M
S
E
M
o
v
i
n
g
a
v
e
r
a
g
e
0
.
0
0
3
2
.
4
1
5
5
e
+
0
7
LO
W
ESS
0
.
0
0
5
2
.
0
7
8
5
e
+
0
7
LO
ESS
0
.
0
0
5
6
.
4
0
9
6
e
+
0
4
S
g
o
l
a
y
0
.
0
0
3
1
.
0
1
3
3
e
-
8
R
LO
W
ESS
0
.
0
0
2
1
.
7
0
3
0
e
-
10
R
LO
ESS
0
.
0
0
2
1
.
7
0
3
0
e
-
10
No
w,
b
ase
d
o
n
AI
C
calcu
lated
au
to
m
atically
f
r
o
m
(
au
to
ar
im
a)
f
u
n
ctio
n
i
n
R
,
it
was
f
o
u
n
d
th
a
t
NARNN
(
2
8
,
1
4
)
p
r
o
d
u
ced
t
h
e
b
est
f
it.
T
ab
le
2
s
h
o
ws
t
h
e
co
m
p
ar
is
o
n
s
a
n
d
th
e
f
in
al
r
esu
lts
o
f
ap
p
l
y
in
g
th
e
h
y
b
r
id
NARNN
an
d
s
m
o
o
th
i
n
g
tech
n
i
q
u
es
f
o
r
t
h
e
L
T
E
b
an
d
wi
d
th
s
lice
f
o
r
ecas
t
f
o
r
s
h
o
r
t
5
0
tim
e
s
tep
s
h
ead
a
n
d
f
o
r
lo
n
g
3
5
0
tim
e
s
tep
s
ah
ea
d
.
T
ab
le
2
al
s
o
s
h
o
ws
th
e
R
MSE
f
o
r
NARNN
o
f
each
s
m
o
o
t
h
in
g
tech
n
iq
u
e
f
o
r
5
0
-
tim
e
s
tep
s
an
d
350
-
tim
e
s
tep
s
.
O
v
er
all,
th
e
h
y
b
r
id
NARNN
te
n
d
ed
to
p
er
f
o
r
m
b
etter
,
with
b
etter
R
MSE
an
d
a
h
ig
h
er
s
m
o
o
t
h
in
g
MSE
.
It
is
wo
r
th
t
o
n
o
te
t
h
at,
th
e
R
MSE
v
alu
es
wh
e
n
ap
p
ly
in
g
NAR
NN
o
n
ly
with
o
u
t
an
y
co
m
b
i
n
ed
tech
n
iq
u
e
wer
e
3
0
8
f
o
r
th
e
5
0
-
tim
e
s
tep
f
o
r
ecast
an
d
3
2
3
f
o
r
t
h
e
3
5
0
-
tim
e
s
tep
.
Fro
m
T
ab
le
2
,
it
is
o
b
v
io
u
s
th
at
th
e
co
m
b
i
n
atio
n
o
f
L
OE
SS
an
d
NARNN
y
ield
ed
b
etter
p
er
f
o
r
m
an
ce
f
o
llo
wed
b
y
th
e
m
o
v
in
g
av
er
ag
e
an
d
NARNN.
T
h
e
Dieb
o
ld
-
Ma
r
ian
o
test
[
2
1
]
-
[
2
3
]
was
th
en
ap
p
lie
d
t
o
ch
ec
k
f
o
r
s
t
atis
tical
s
ig
n
if
ican
ce.
NARNN
with
L
OE
SS
R
MSE
was
f
o
u
n
d
t
o
b
e
s
tatis
tically
d
if
f
er
en
t
f
r
o
m
o
th
er
h
y
b
r
id
tech
n
i
q
u
es.
T
h
e
s
am
e
f
in
d
in
g
was
f
o
u
n
d
f
o
r
th
e
3
5
0
tim
e
s
tep
f
o
r
ecast.
T
h
er
ef
o
r
e,
NARNN
with
L
OE
SS
y
ield
ed
b
ette
r
p
er
f
o
r
m
an
ce
an
d
was
v
er
if
ie
d
s
tatis
tically
v
ia
th
e
Dieb
o
ld
-
Ma
r
ian
o
test
as
well.
T
h
is
r
esu
lt
co
n
f
ir
m
s
th
e
ef
f
ecti
v
en
ess
an
d
th
e
r
eliab
ility
o
f
th
e
h
y
b
r
id
NARNN
an
d
th
e
s
m
o
o
th
i
n
g
t
ec
h
n
iq
u
es
f
o
r
f
o
r
ecastin
g
s
h
o
r
t
-
an
d
lo
n
g
-
ter
m
s
cales.
T
h
e
au
to
co
r
r
elatio
n
f
u
n
ct
io
n
(
AC
F)
o
b
tai
n
ed
u
s
in
g
t
h
e
L
ju
n
g
–
B
o
x
test
was
u
s
ed
f
o
r
f
u
r
th
er
an
aly
s
is
.
T
h
e
an
aly
s
is
o
f
AC
F
was
u
s
ed
to
calc
u
late
th
e
n
u
m
b
er
o
f
in
p
u
ts
o
f
au
to
-
co
r
r
elated
v
ecto
r
s
to
cr
eate
a
n
ap
p
r
o
p
r
iate
m
o
d
el.
Mo
r
eo
v
er
,
it
was
also
u
s
ed
t
o
in
v
esti
g
ate
wh
ite
n
o
is
e
(
zer
o
m
ean
,
co
n
s
tan
t
v
ar
ian
ce,
u
n
co
r
r
elated
p
r
o
cess
es,
a
n
d
n
o
r
m
ally
d
is
tr
ib
u
ted
)
in
th
e
r
esid
u
als.
Fig
u
r
e
2
(
a)
s
h
o
ws
th
e
AC
F
an
d
t
h
e
p
lo
ts
o
f
t
h
e
r
e
s
id
u
als
o
f
t
h
e
h
y
b
r
id
NARNN
s
m
o
o
th
in
g
f
o
r
ecast
m
o
d
els
f
o
r
t
h
e
5
0
-
tim
e
s
tep
.
An
d
Fig
u
r
e 2
(
b
)
f
o
r
3
5
0
-
tim
e s
tep
a
h
ead
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
A
n
a
lysi
s
o
f h
yb
r
id
n
o
n
-
lin
ea
r
a
u
to
r
eg
r
ess
ive
n
eu
r
a
l n
etw
o
r
k
a
n
d
… (
Mo
h
a
med
K
h
a
l
a
fa
lla
Ha
s
s
a
n
)
1085
(
a)
(
b
)
(
c)
Fig
u
r
e
1
.
B
an
d
wid
th
u
tili
za
tio
n
u
s
in
g
m
o
v
in
g
av
ar
a
g
e:
(
a)
o
r
ig
in
al
L
T
E
s
lice
,
(
b
)
L
T
E
s
lice
s
m
o
o
th
e
d
with
q
=0
.
0
0
3
,
an
d
(
c)
L
T
E
s
lice
s
m
o
o
th
ed
with
q
=
0
.
0
5
T
ab
le
2
.
R
MSE
r
esu
lts
o
f
ap
p
l
y
in
g
th
e
h
y
b
r
id
tech
n
i
q
u
es
S
mo
o
t
h
i
n
g
Te
c
h
n
i
q
u
e
q
R
M
S
E
o
f
5
0
-
t
i
me
st
e
p
s
a
h
e
a
d
f
o
r
e
c
a
s
t
u
si
n
g
N
A
R
N
N
+
sm
o
o
t
h
i
n
g
R
M
S
E
o
f
3
5
0
-
t
i
m
e
s
t
e
p
s
a
h
e
a
d
f
o
r
e
c
a
st
u
si
n
g
N
A
R
N
N
+
sm
o
o
t
h
i
n
g
M
o
v
i
n
g
A
v
e
r
a
g
e
0
.
0
0
3
2
7
2
2
9
5
LO
W
ESS
0
.
0
0
5
2
8
9
3
3
0
LO
ESS
0
.
0
0
5
2
7
0
2
9
3
S
g
o
l
a
y
0
.
0
0
3
3
0
9
3
5
1
R
LO
W
ESS
0
.
0
0
2
2
9
2
3
4
0
R
LO
ESS
0
.
0
0
2
2
8
9
2
9
8
Evaluation Warning : The document was created with Spire.PDF for Python.
I
SS
N
:
1
6
9
3
-
6
9
3
0
T
E
L
KOM
NI
KA
T
elec
o
m
m
u
n
C
o
m
p
u
t E
l Co
n
tr
o
l
,
Vo
l.
19
,
No
.
4
,
Au
g
u
s
t 2
0
2
1
:
1
7
0
8
-
1
0
8
9
1086
(
a)
(
b
)
Fig
u
r
e
2
.
T
h
e
AC
F
a
n
d
th
e
p
lo
t
s
o
f
th
e resid
u
als
o
f
t
h
e h
y
b
r
id
NARNN
s
m
o
o
th
in
g
f
o
r
ecast
m
o
d
els
f
o
r
:
(
a)
th
e 5
0
-
tim
e s
tep
an
d
(
b
)
3
5
0
-
tim
e s
tep
I
n
th
e
ca
s
e
o
f
th
e
5
0
-
tim
e
s
tep
f
o
r
ec
ast
u
s
in
g
th
e
h
y
b
r
id
NARNN
with
L
OE
S
S
,
th
e
r
esid
u
als
f
ell
r
an
d
o
m
l
y
with
in
th
e
h
o
r
izo
n
tal
b
an
d
(
b
etwe
en
4
e7
an
d
-
4
e7
)
an
d
as
a
r
esu
lt
th
e
v
ar
ian
ce
o
f
t
h
e
r
esid
u
als
lo
o
k
ed
to
b
e
in
d
ep
e
n
d
en
t
o
f
th
e
s
ize
o
f
th
e
f
itted
v
alu
es.
Me
a
n
wh
ile,
th
e
s
am
e
r
esu
lts
wer
e
f
o
u
n
d
f
o
r
3
5
0
-
tim
e
s
tep
s
f
o
r
ec
ast in
h
y
b
r
id
NARNN
.
T
h
is
p
atter
n
s
u
g
g
ests
th
at
th
e
v
a
r
ian
ce
s
in
th
e
er
r
o
r
ter
m
s
ar
e
e
q
u
al.
Mo
r
eo
v
er
,
n
o
o
n
e
r
esid
u
al
s
to
o
d
o
u
t
f
r
o
m
t
h
e
r
an
d
o
m
p
atter
n
;
th
u
s
,
s
u
g
g
esti
n
g
th
at
th
er
e
wer
e
n
o
o
u
tli
er
s
.
T
h
e
lag
s
in
t
h
e
AC
F
p
lo
ts
f
ell
b
elo
w
th
e
0
.
0
8
th
r
esh
o
ld
.
Mo
r
e
o
v
er
,
n
o
p
atte
r
n
was
ev
id
e
n
t
in
t
h
e
r
esid
u
al
s
.
Ad
d
itio
n
ally
,
t
h
e
r
esid
u
als
f
o
llo
wed
a
r
an
d
o
m
d
is
tr
ib
u
tio
n
ar
o
u
n
d
ze
r
o
.
T
h
is
r
esu
lt
co
n
f
ir
m
s
an
d
v
alid
ates
th
at
th
e
NARNN
with
L
OE
SS
r
elat
iv
ely
p
r
o
v
id
ed
t
h
e
b
est
f
o
r
ec
asti
n
g
m
o
d
els.
Fi
g
u
r
e
3
(
a)
s
h
o
ws
th
e
p
er
f
o
r
m
an
ce
co
m
p
ar
is
o
n
o
f
h
y
b
r
id
NARNN
v
er
s
u
s
h
y
b
r
i
d
Seaso
n
al
Au
to
r
eg
r
ess
iv
e
Mo
v
i
n
g
Av
er
ag
e
(
SAR
I
MA
)
f
o
r
5
0
-
tim
e
s
tep
f
o
r
ec
ast,
th
e
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d
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s
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en
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iq
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h
er
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r
e
,
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L
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wi
ll
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e
o
u
r
b
est
ch
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ice
s
in
ce
o
u
r
o
b
jectiv
e
is
to
p
r
o
v
i
d
e
b
est f
o
r
ec
ast p
e
r
f
o
r
m
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ce
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m
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ata
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e
as d
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s
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ed
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lier
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e
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in
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o
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th
e
3
5
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o
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ec
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Fig
u
r
e
3
(
b
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(
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u
r
e
3
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ce
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d
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200
400
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a
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0
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0
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10
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re
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r
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d
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ir
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s
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e
s
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p
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th
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r
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o
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d
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4
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