Indonesi
an
Journa
l
of El
ect
ri
cal Engineer
ing
an
d
Comp
ut
er
Scie
nce
Vo
l.
9
, No
.
2
,
Febr
ua
ry
201
8
,
pp.
410
~
416
IS
S
N:
25
02
-
4752
, DO
I: 10
.11
591/
ijeecs
.
v9.i
2
.
pp
410
-
416
410
Journ
al h
om
e
page
:
http:
//
ia
es
core.c
om/j
ourn
als/i
ndex.
ph
p/ij
eecs
Alternat
ive M
ethods for F
orecasti
ng Varia
tions in
Hos
pit
al Bed
Admi
ssion
S.Sari
f
ah
Rad
iah Shari
ff
1
,
Mohd
Az
ua
n
Suh
aimi
2
, S
iti
Meriam
Z
ah
ar
i
3
,
Z
uraida
h
Derasi
t
4
1
Malay
s
ia Insti
tu
te
of
Tr
ansport
(
MITRAN
S),
Univer
siti
T
eknol
o
gi
MA
RA Shah A
la
m
,
Mal
a
y
s
ia
2
,
3
,
4
Cent
re
for
St
at
isti
cs
and
Dec
i
sion Sc
ie
n
ce,
Fa
cul
t
y
of
Com
put
er
&
Math
ematica
l
Scie
n
ce
s,
Univer
siti
T
ekno
logi
MA
RA,
404
50
Shah
Alam,
Sela
ngor
,
Ma
lay
si
a
Art
ic
le
In
f
o
ABSTR
A
CT
Art
ic
le
history:
Re
cei
ved
Oct
1
9
, 201
7
Re
vised
Dec
2
7
, 2
01
7
Accepte
d
Ja
n
1
8
, 2
01
8
The
Mal
a
y
s
ia
n
hea
l
thc
ar
e
s
y
s
tem
is
well
-
bei
ng
rec
ogni
ze
d
for
providi
ng
a
wide
ran
ge
of
acce
ss
to
primar
y
hea
l
thc
ar
e.
Th
e
num
ber
of
hospi
ta
ls
is
found
to
be
growing
in
li
n
e
with
th
e
inc
r
ea
se
in
p
opula
ti
on
.
How
eve
r,
over
-
cro
wding
has
b
ec
om
e
th
e
m
ost
comm
on
sce
ne
that
peop
le
se
e
in
ev
e
r
y
hospita
l
.
The
n
um
ber
of
pat
i
e
nts
bei
ng
admit
te
d
m
a
y
som
ehow
m
isle
ad
hea
l
thc
ar
e
pla
nn
ers,
and
thus
caus
ing
the
m
to
under
esti
m
ate
the
resourc
es
tha
t
ar
e
req
u
ire
d
withi
n
the
hosp
it
al
.
Thus,
thi
s
stud
y
ai
m
s
to
identif
y
better
fore
ca
st
ing
m
odel
s
for
var
ia
t
ions
in
hospita
l
bed
admiss
ion
conside
ring
State
Space
Model
(
SS
M).
Data
on
the
admiss
ion
rat
e
of
a
state
hospita
l
wa
s
col
l
ec
t
ed,
spann
ing
the
per
iod
o
f
histori
cal
data
from
2001
unti
l
2015.
The
findi
ngs
indi
c
ate
tha
t
Sta
te
Spa
ce
m
odel
ca
n
outp
erf
orm
comm
on
m
odel
due
to
it
s
lower
Mea
n
Square
d
Err
ors.
Fem
al
e
age
d
bet
wee
n
25
-
34
y
ea
rs
old
are
found
to
be
havi
ng
the
highe
st varia
ti
on
,
which
co
uld
le
ad
to
unpre
dic
t
abl
e
i
n
te
rm
s of
be
ing a
dm
it
te
d
to
hospit
al
.
Ke
yw
or
d
s
:
Fo
r
ecast
ing Va
riat
ion
s
Stat
e Sp
ace M
od
el
(SSM
)
Copyright
©
201
8
Instit
ut
e
o
f Ad
vanc
ed
Engi
n
ee
r
ing
and
S
cienc
e
.
Al
l
rights re
serv
ed
.
Corres
pond
in
g
Aut
h
or
:
S.S
ari
fah Ra
di
ah
S
ha
riff
Malay
s
ia Insti
tu
t
e
of Transport
(
MITRAN
S),
Univer
siti
Te
kno
logi
MA
RA Sha
h
Alam
,
Ma
lay
si
a
Em
a
il
: l
sn
tl
@c
cu.
e
du.tw
1.
INTROD
U
CTION
Nowa
days,
in
the
m
od
er
n
w
or
l
d,
pe
ople
fa
ced
the
chall
e
ng
e
s
an
d
vola
ti
le
ye
ar
fo
r
li
vin
g
co
sts
in
their d
ai
ly
li
fe.
D
ue
on
the
inc
reasin
g
a
nd h
ig
her
pri
ce of
t
re
atm
ent
and
m
e
dicine for
healt
hcar
e
,
m
any
shi
fted
to
ha
ve
the
tre
atm
ent
in
gove
rn
m
ent
ho
s
pital
becau
se
of
t
he
lo
wer
pr
ic
e
rates.
T
he
inc
rease
of
th
os
e
w
ho
com
e
to
get
serv
ic
es
f
ro
m
the
governm
ent
ho
s
pital
is
an
im
po
rtant
i
ssu
e
that
can
le
ad
to
the
shorta
ge
for
the
total
of
be
d
a
dm
issi
on
in
the
governm
ent
ho
s
pital
.
A
ris
e
in
disease
pro
gr
e
ssio
n
rate
s
al
so
can
le
a
d
to
a
trem
end
ou
s
in
crease
in
the
num
ber
of
hos
pi
ta
l
bed
adm
issio
n,
res
ulti
ng
in
hig
h
m
edical
exp
e
ns
es
.
Fro
m
day
-
t
o
-
day,
the
tot
al
s
of
people
wh
ic
h
a
re
trea
te
d
at
ho
s
pital
are
i
ncr
ea
sin
g
an
d
it
is
nece
ssary
f
or
Mi
ni
stry
of
Healt
h
(MO
H
)
to
plan
ca
re
fu
ll
y
about
th
e
nu
m
ber
of
bed
a
dm
issi
on
to
avo
id
c
on
gestio
n
an
d
sh
ort
age
pro
blem
in
governm
ent
healt
hcar
e
facil
it
y.
Re
la
te
d
with
the
risin
g
in
co
ns
um
er
de
m
and
s,
the
plan
ni
ng
of
ho
s
pital
be
d
a
dm
issi
on
is
ve
ry
i
m
po
rta
nt
to
e
ns
ure
that
i
t
giv
es
t
he
po
sit
ive
consi
derable
im
plications
f
or
ho
s
pital
resou
r
ce
al
locat
ion
.
The
hos
pital
plann
e
rs
m
us
t
c
reati
vely
adjus
t
the
i
m
po
rtan
t
el
e
m
ents
su
ch
as
ho
s
pital
be
ds
,
sta
ff
in
g
le
vels,
m
edici
ne
us
a
ges
a
nd
ot
her
relat
ed
re
sourc
es.
He
nce,
it
is
ve
ry
im
po
rtant
to
app
ly
su
it
able
forecast
in
g
m
e
thods
in
or
der
to
op
ti
m
al
l
y
manag
e
hosp
it
al
bed
a
dm
issi
o
ns
an
d
ot
her
r
el
at
ed
healt
hcar
e
ser
vices.
The
go
od
f
or
ec
ast
ing
m
od
el
will
pl
ay
a
sig
nifica
nt
r
ole
in
the
eff
ic
ie
nt
al
loca
ti
on
of
resou
rces
in
he
al
thcare
syst
em
s
with
con
str
ai
ned
budget
s.
It
al
so
can
hel
p
the
hosp
it
al
m
anag
em
ent
syst
e
m
s
in or
der
t
o op
ti
m
al
l
y
m
anag
e
patie
nt f
l
ow and to
im
pr
ov
e
m
anag
em
ent st
ra
te
gies, effici
en
cy
an
d safet
y.
Re
la
te
d
with
the
go
od
forec
ast
ing
m
et
ho
d
for
f
or
ecast
in
g
va
riat
ion
s
i
n
num
ber
of
ho
s
pital
be
d
adm
issi
on
,
ARIMA
m
od
el
ha
ve
bee
n
a
pp
li
e
d
in
a
fe
w
of
previ
ou
s
stu
dies
w
hich
f
ocus
on
bed
op
ti
m
iz
a
ti
on
,
bed
ca
pacit
y
and
be
d
adm
is
si
on.
H
oweve
r,
i
ts
identific
at
io
n
te
ch
niques
s
ee
m
diff
ic
ult
a
nd
c
om
plex
in
order
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Alt
erna
ti
ve Me
thods f
or
F
or
e
castin
g
V
ar
iati
on
s
in
Hos
pital Bed
Ad
missio
n
(
S.
Sa
rif
ah
R
ad
i
ah Sh
ar
if
f
)
411
to
identify
the
correct
m
od
el
from
the
cl
ass
of
possi
ble
m
od
el
s.
This
m
od
el
al
so
co
m
es
up
with
theo
re
ti
cal
m
od
el
and
str
uc
tural
relat
io
nships
w
hich
are
no
t
disti
nct
wi
th
oth
e
r
sim
ple
forecast
m
od
el
s.
ARIM
A
m
od
el
s
al
so
essenti
al
ly
back
wa
rd
lo
ok
i
ng
a
nd
it
reasons
that
it
al
ways
poor
wh
e
n
predict
i
ng
se
ries
with
turn
in
g
po
i
nts.
S
o,
in
con
t
ro
ll
in
g
a
nd
op
ti
m
izing
t
he
governm
ent
exp
e
ndit
ur
e
on
healt
hca
re
syst
e
m
at
the
public
ho
s
pital
s
,
the
re
is
a
nee
d
to
pro
pose
a
good
forecast
in
g
m
e
thod
a
nd
it
s
al
t
ern
at
ives
f
or
the
best
strat
eg
y
an
d
plan
ning
in
e
stim
ating
the
healt
hcare
s
ources,
pa
rtic
ularly
the
vari
at
ion
s
in
nu
m
ber
of
ho
s
pi
ta
l
bed
adm
issi
on
s.
Pa
st
stud
ie
s
that
us
e
d
ARIMA
can
be
fou
nd
in
[1,2,3
,
4].
Q
ueu
i
ng
T
heory
is
al
so
a
ppli
ed
t
o
pr
e
dict
m
on
thl
y
resp
onsiv
ene
ss
for
cha
ng
i
ng
be
d
relat
ed
with
cha
ng
i
ng
bed
dem
and
[5,6
,
7,8,9]
.
Stat
e
Sp
ace
Mod
el
(S
SM
)
is
known
as
t
he
m
od
el
wh
ic
h
inclu
des
t
wo
m
ajo
r
el
em
ent
s:
an
obser
vation
pro
cess
a
nd
al
s
o
a
sta
te
pr
ocess
.
I
t
is
kn
own
as
on
e
m
od
el
whic
h
has
powe
rful
fr
am
ewo
r
k
for
the
pur
po
s
e
of
analy
sis
fo
r
t
he
dynam
ic
al
s
yst
e
m
s.
Hen
ce,
this
stud
y
at
te
m
pts
to
app
ly
SSM
to
fore
cast
var
ia
ti
on
in
nu
m
ber
of
be
d
adm
issi
on
.
2.
RESEA
R
CH MET
HO
D
In
sta
te
sp
ace
m
od
el
s,
there
are
three
ty
pes
of
in
fer
e
nce
wh
ic
h
al
ways
app
li
ed
f
or
thi
s
m
od
el
w
hich
are
pr
e
dicti
on, fi
lt
ering
an
d
s
m
oo
thing
.
In
ge
ner
al
,
the stat
e sp
ace
m
od
el
is w
ritt
en
a
s fo
ll
ow
s:
Stat
e equ
at
i
on
or tran
sit
ion
e
quat
ion
:
)
,
0
(
~
1
t
t
t
t
t
Q
iid
η
,
η
R
c
T
t
t
t
Me
asur
em
ent o
r
o
bs
e
rv
at
io
n equ
at
io
n:
)
,
0
(
~
,
t
t
t
t
H
i
i
d
t
t
t
d
Z
y
In
it
ia
l st
at
e d
is
tribu
ti
on:
)
,
(
~
0
0
0
P
a
α
N
wh
e
re
t
Z
is
an
N
x
m
m
a
trix,
t
d
is
an
N
x
1
ve
ct
or
a
nd
t
is
an
N
x
1
e
rro
r
ve
ct
or
,
t
T
is
an
m
x
m
transiti
on
m
at
r
ix,
t
c
is
an
m
x
1
vecto
r,
t
R
is
a
m
x
g
m
at
rix,
an
d
t
η
is
a g
x
1
e
rro
r
ve
ct
or.
T
he
m
at
rices
t
t
t
t
t
t
R
,
c
,
T
,
H
,
d
,
Z
and
t
Q
an
d
co
ntains
no
nr
a
ndom
el
e
m
e
nts.
The
assum
ption
s
of
the
m
od
el
are
li
ste
d
as foll
ows:
i)
The
dist
urban
c
es
of
ε
t
an
d
η
t
are
unco
rr
el
at
ed
with
the
i
ni
ti
al
s
ta
te
var
ia
ble
an
d
al
so
un
c
orrelat
ed
wi
th each ot
her
f
or all
tim
e p
eriod
s
.
ii)
The
i
niti
al
vector
α
0
has
a
m
ea
n
of
α
0
:
E(
α
0
)
=
α
0
an
d
c
ov
a
riance
m
at
rix
of Ʃ
0
:
Var(
α
0
)
=
Ʃ
0.
iii)
The
distu
r
bances
of
ε
t
and
η
t
are
no
rm
al
l
y
distribu
te
d
a
nd
se
rial
ly
ind
epende
nt
wit
h
const
ant
var
ia
nc
es.
2.1 Dia
gnost
ic
C
hec
ks
All
sign
ific
a
nc
e
te
st
and
const
ru
ct
io
n
of
confide
nce
inte
rv
al
s
in
Stat
e
Sp
ace
Mo
del
rely
on
th
e
assum
ption
s
w
hich
are
relat
e
d
to
resid
ual
analy
sis
includi
ng
norm
al
i
ty
,
ho
m
os
cedasti
c
it
y
and
ind
epe
nd
e
nce.
Anothe
r
diag
nosti
c
too
l
for
de
te
rm
ining
the
appr
opriat
ene
ss
of
the
m
od
e
l
is
known
as
‘auxil
ia
ry
resi
du
al
s
’.
The
a
uxil
ia
ry
r
esi
du
al
s
can
be
ap
plied
f
or
the
pur
po
s
e
of
detect
ing
outl
ie
rs
a
nd
str
uctu
ral
brea
ks
bec
ause
ε
̂
t
and
η
̂
t
are
the
e
stim
at
or
of
ε
t
and
η
t
.
The
s
m
oo
th
obser
ve
d
dist
urban
ce
s
of
∗
ena
ble
for
the
detect
ion
of
ou
tl
ie
r
obser
va
ti
on
s.
For
s
m
oo
th
sta
te
disturba
nces,
it
al
lows
the
detect
ion
of
struct
ur
al
breaks
i
n
dev
el
op
m
ent of ti
m
e series.
Fo
r
Stat
e
S
pac
e
Mo
del
ap
plica
ti
on
,
pac
ka
ge
s
in
R
cal
le
d
Stru
ct
TS
an
d
dlm
are
us
e
d.
At
the
sam
e
tim
e,
a
com
mo
n
f
or
ecast
i
ng
m
od
el
,
ARIM
A
was
r
un
to
validat
e
the
re
su
lt
s.
ARIMA
m
od
el
was
r
un
us
in
g
Eviews
.
2.2 Da
ta c
ollec
tion
In
this
stu
dy,
ho
s
pital
bed
a
dm
issi
on
data
base
d
on
ge
nder
an
d
age
gr
oups,
co
ver
i
ng
t
he
pe
rio
d
of
2001
unti
l
2015
is
colle
ct
ed
f
ro
m
a
sta
te
ho
sp
it
al
in
Ma
la
ys
ia
.
The
age
dat
aset
is
ran
ge
d
accor
ding
to
th
e
data
so
urce
as
0
-
4,
5
-
19,
20
-
24,
25
-
34,
35
-
44,
45
-
54,
55
-
64,
65
-
74,
75
-
84,
75+
.
H
ow
e
ve
r,
the
re
are
m
issi
ng
values
of
total
adm
issi
on
data,
pa
rt
ic
ularly
duri
ng
the
ea
rly
ye
ar
s
of
st
ud
y
dur
at
ion
.
To
ha
nd
le
the
m
issi
ng
data,
Am
elia
II
pac
kag
e
dev
el
ope
d
by
Profe
ssor
Gar
y
King
f
r
om
Har
vard
U
niv
e
rsity
is
being
util
iz
ed
in
the
R
Dev
el
op
m
ent
Core
Team
so
f
tware
pa
cka
ge
ver
si
on
3.2.3.
The
Am
el
ia
II
R
pack
a
ge
is
a
n
up
dating
versi
on
of
the
Am
elia
fir
st
ve
rsion.
It
runs
a
f
orm
of
the
bootstra
p
-
base
d
EM
a
lgorit
hm
to
pe
rfor
m
the
m
ulti
ple
i
m
pu
ta
ti
on
te
c
hn
i
qu
e
t
hat
ha
s
the
abili
ty
to
com
pu
te
m
a
ny
m
or
e
var
ia
bles
that
com
e
with
m
any
m
or
e
ob
s
er
vations, i
n
c
onsidera
bly
faster t
han exis
ti
ng
a
ppr
oach
e
s [10,1
1].
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.
9
,
No.
2
,
Fe
br
uary
201
8
:
410
–
416
412
3.
RESU
LT
S
AND A
N
ALYSIS
The
res
ults
are
discu
ssed
in
sever
al
phases:
app
li
cat
ion
of
m
od
el
s,
analy
sis
of
var
ia
ti
on
s
a
nd
perform
ance m
easur
em
ent.
3.1
Results
f
r
om
AR
I
M
A
m
od
e
l
The
re
su
lt
f
rom
ARIMA
m
od
el
us
in
g
E
views
wa
s
obta
ined
first
in
order
t
o
chec
k
a
nd
c
ollec
t
m
ore
con
cl
us
ive
e
vi
den
ce
a
bout
th
e
data
sta
ti
on
a
rity
con
diti
on.
The
ACF
(Autoc
orrelat
ion
Functi
on)
an
d
PA
CF
(P
arti
al
Au
t
oc
orrelat
ion
F
unct
ion
)
we
re
al
s
o
plo
tt
ed
to
de
te
rm
ine
the
s
pe
ci
ficat
ion
of
ARIMA
m
od
e
l.
From
Figure
1,
the
c
hanges
vecto
rs
of
th
e
a
uto
c
orrelat
ion
are
de
creasin
g
as
the
tim
e
increases
,
and
s
om
e
even
m
e
e
t
to
ne
gative
val
ues.
From
the
gr
a
ph,
four
val
ues
of
the
a
utoc
orrelat
ion
s
ex
ceed
the
sig
nif
ic
ance
li
m
it
.
Hen
ce
,
there
is
a
need
for
this
se
ries
to
be
m
ade
sta
ti
on
ary
by
pe
rfor
m
ing
the
first
dif
fer
e
nce.
Figure
1
sho
w
s
AC
F
gr
a
ph fo
r
total
of b
e
d
a
dm
issio
n.
Figure
1. ACF
Gr
a
ph fo
r
T
otal of Be
d A
dm
is
sion
Perfo
r
mi
ng Fi
rst Differe
ncing
Fr
om
Figure
2,
we
can
see
t
ha
t
the
gr
a
ph
showi
ng
t
he
dra
m
at
ic
decayi
ng
for
the
data.
It
is
no
t
sho
wing
the slo
wing m
ov
e
up o
r dow
n from
the g
ra
ph. So,
it
is co
nclu
ded that t
he
d
at
a
now
is
s
ta
ti
on
ary.
Figure
2.
ACF
yt
-
1 Gr
a
ph
3
5
3
0
2
5
2
0
1
5
1
0
5
1
1
.
0
0
.
8
0
.
6
0
.
4
0
.
2
0
.
0
-
0
.
2
-
0
.
4
-
0
.
6
-
0
.
8
-
1
.
0
L
a
g
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
F
u
n
c
t
i
o
n
f
o
r
T
o
t
a
l
O
f
B
e
d
A
d
m
i
s
s
i
o
n
(
w
i
t
h
5
%
s
i
g
n
i
f
i
c
a
n
c
e
l
i
m
i
t
s
f
o
r
t
h
e
a
u
t
o
c
o
r
r
e
l
a
t
i
o
n
s
)
3
5
3
0
2
5
2
0
1
5
1
0
5
1
1
.
0
0
.
8
0
.
6
0
.
4
0
.
2
0
.
0
-
0
.
2
-
0
.
4
-
0
.
6
-
0
.
8
-
1
.
0
L
a
g
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
A
u
t
o
c
o
r
r
e
l
a
t
i
o
n
F
u
n
c
t
i
o
n
f
o
r
y
t
-
1
(
w
i
t
h
5
%
s
i
g
n
i
f
i
c
a
n
c
e
l
i
m
i
t
s
f
o
r
t
h
e
a
u
t
o
c
o
r
r
e
l
a
t
i
o
n
s
)
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
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c Eng &
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m
p
Sci
IS
S
N:
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02
-
4752
Alt
erna
ti
ve Me
thods f
or
F
or
e
castin
g
V
ar
iati
on
s
in
Hos
pital Bed
Ad
missio
n
(
S.
Sa
rif
ah
R
ad
i
ah Sh
ar
if
f
)
413
The
data
m
ay
no
t
pe
rf
ect
ly
sta
ti
on
ary
beca
use
in
ec
onom
ic
or
bu
si
ness
da
ta
series
s
uc
h
conditi
on
m
ay
no
t
be
ea
sil
y ac
hieva
ble
du
e
to
the
explai
na
bl
e factors in
he
r
ent in t
he data
set
s.
Model
Ide
nt
ifi
cat
i
on
In
ord
er
t
o
i
de
ntify
the
best
a
nd
s
uitable
m
od
el
,
t
he
a
naly
sis
of
the
AC
F
and
P
ACF
gra
ph
s
wer
e
do
ne
and
f
our
m
od
el
s
hav
e
bee
n
identifie
d
an
d
e
stim
at
ed
us
ing
Eviews
w
hich
are
AR
IMA
(
2,1,2)
,
AR
IM
A
(2,1,0
),
ARIM
A
(1,1,1
)
a
nd
ARIMA
(
1,1,0
).
By
c
om
par
ing
the
m
od
el
s
in
Ta
ble
1,
t
he
best
m
od
el
i
s
ARIMA
(1,
1,1
)
du
e
it
s sm
alle
st M
SE =
5003
72.
Table
1.
Su
m
m
ary o
f
P
ort
m
an
te
au
Test
Statistics
Mod
el
ARIMA
(2,1
,2)
ARIMA
(2,1
,0)
ARIMA
(1,1
,1)
ARIMA
(1,1
,0)
Calcu
lated
Q
1
0
.2
3
1
.3
1
6
.1
3
4
.6
DF
7
9
9
10
Tabu
lated
Q
1
4
.06
1
6
.91
1
6
.91
1
8
.30
Decisio
n
(
5
% sig
lev
el)
Accept
Ho
Reject Ho
Accept Ho
Reject Ho
Co
n
clu
sion
The er
rors ar
e whit
e
n
o
ise
The er
rors ar
e
n
o
t
wh
ite no
ise
The er
rors ar
e whit
e
n
o
ise
The er
rors ar
e
n
o
t
wh
ite no
ise
MSE
5
0
2
2
8
3
6
0
1
8
5
5
5
0
0
3
7
2
6
4
9
1
4
1
3.2 State
Sp
ac
e M
od
el
li
ng
Stru
ct
TS
pac
ka
ge
in
R
is
kn
own
as
Str
uctu
ral
tim
e
serie
s
m
od
el
s
in
Sta
te
Sp
ace
M
od
e
l,
is
ap
plied
for
est
im
ating
the
pa
ram
et
ers
of
sim
ple
Stat
e
Sp
ace
Mo
de
l
for
eac
h
a
ge
gro
up
s
of
be
d
adm
issi
on
.
F
or
this
stud
y,
this
pac
kag
e
is
s
uitabl
e
becau
s
e
the
dataset
for
hos
pital
bed
a
dm
i
ssion
is
un
i
vari
at
e
tim
e
serie
s
and
base
d
on
10
a
ge
groups
bas
ed
on
ge
nder
(m
al
e
and
fem
al
e).
It
c
onstr
uc
ts
a
local
li
ne
ar
tre
nd
m
od
el
a
nd
est
i
m
at
es
the
par
am
et
ers
fo
r
ho
s
pital
bed
adm
issi
on
fo
r
each
age
gro
up
s
.
Table
2
sh
ows
the
est
i
m
at
e
par
am
et
ers
for
local
li
near
tr
end
m
od
el
f
or
m
al
e
with
10
a
ge
gr
oups
for
ho
s
pital
be
d
a
dm
issi
on
.
Fro
m
Table
2,
it
can
be
see
n
that
the
high
est
transiti
on
al
var
ia
nce
(le
ve
l)
values
is
on
age
gr
oups
5
-
19
ye
ars
old
whic
h
is
403.7
0
an
d
f
or
ob
se
r
vational
var
ia
nce
(e
ps
il
on),
a
ge
gro
up
s
of
3
5
-
44
ye
a
rs
ol
d
ha
ve
the
highest
values
with
18808.0
2.
The
value
of
transiti
onal
vari
ance
re
fers
to
the
m
axi
m
u
m
li
kelihoo
d
est
i
m
at
es
(MLEs)
f
or
le
ve
l
,
wh
il
e
f
or
obse
rv
at
io
nal
va
riance
is
the
val
ue
(MLEs)
of
obser
vatio
n
er
ror
va
riances
(epsi
lon
)
.
It
m
eans
t
hat
wh
e
n
bo
t
h
of
t
hese
values
a
re
high,
th
ere
is
huge
var
ia
ti
on
in
the
nu
m
ber
of
be
d
bei
ng
a
dm
i
tt
ed.
This
i
s
quit
e
crit
ic
al
becau
s
e
the
hu
ge
va
r
ia
ti
on
is
crit
ic
al
and
will
m
a
ke
the
forecast
ing
process
ha
rd
e
r.
Huge
vari
at
ion
occurs
f
or
a
ge gr
oup 3
5
-
44 ye
ars
old
f
or
m
ale
gro
up.
Table
2.
E
stim
at
e Param
et
ers
for
L
ocal Li
ne
ar T
rend M
od
e
l (Mal
e)
Ag
e Gr
o
u
p
s
Tr
an
sitio
n
al
v
ariance (
lev
el
)
Slo
p
e variance
Ob
serv
atio
n
al
v
ariance (
ep
silo
n
)
Initial lev
el of
mu
Initial lev
el of
la
m
b
d
a
Less th
an
1
3
4
6
.35
0
7
1
2
.27
154
0
1
-
4
7
9
.93
0
3
8
2
.44
97
0
5
-
19
4
0
3
.70
0
3
1
2
3
.7
3
272
0
20
-
24
1
4
4
.65
0
3
3
8
.13
96
0
25
-
34
9
7
.87
0
1
1
4
9
.2
4
146
0
35
-
44
0
0
1
8
8
0
8
.02
151
0
45
-
54
9
0
.57
0
1
4
6
7
.9
5
149
0
55
-
64
3
1
.87
0
4
0
0
4
.2
1
183
0
65
-
74
1
0
.32
0
5
0
6
3
.4
4
145
0
More than
75
2
5
.47
0
1
8
4
8
.6
3
86
0
The
est
im
a
ti
on
of
pa
ram
et
ers
for
local
li
near
trend
m
od
el
is
al
so
done
f
or
f
e
m
al
e
wh
ic
h
al
so
ha
ve
10
age
gr
oups
.
From
Table
3,
th
e
highest
val
ue
s
for
tra
ns
it
iona
l
var
ia
nce
(le
vel)
a
nd
al
s
o
obser
vatio
nal
va
riance
(ep
sil
on
)
com
es
from
age
gro
up
25
-
34
ye
a
rs
o
ld
with
val
ue
s
of
2280.
85
a
nd
2125
4.09.
It
m
eans
that
the
huge
var
ia
ti
on
occ
urs
f
or
t
his
age
group.
It
sho
ws
that
this
a
ge
gro
up
is
m
or
e
un
pr
e
dicta
bl
e
in
te
rm
s
of
hav
i
ng
them
b
ei
ng
a
dm
itted to
t
he h
os
pital
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
2
,
Fe
br
uary
201
8
:
410
–
416
414
Table
3.
E
stim
at
e Param
et
ers
for
L
ocal Li
ne
a
r
T
rend M
od
e
l (Fem
al
e)
Ag
e Gr
o
u
p
s
Tr
an
sitio
n
al
v
ariance (
lev
el
)
Slo
p
e variance
Ob
serv
atio
n
al
v
ariance (
ep
silo
n
)
Initial lev
el of
mu
Initial lev
el of
la
m
b
d
a
Less th
an
1
3
8
0
.85
0
5
2
2
.82
149
0
1
-
4
4
7
.33
0
2
4
7
.89
71
0
5
-
19
4
6
1
.40
0
2
2
1
4
.9
5
227
0
20
-
24
5
2
4
.01
0
3
3
5
9
.4
1
336
0
25
-
34
2
2
8
0
.8
5
0
2
1
2
5
4
.09
898
0
35
-
44
1
3
1
0
.9
6
0
1
4
7
1
2
.55
553
0
45
-
54
9
0
.57
0
1
4
6
7
.9
5
149
0
55
-
64
7
5
.84
0
8
6
2
.47
127
0
65
-
74
1
5
.36
0
3
1
2
1
.5
2
77
0
More than
75
9
.26
0
8
8
2
.25
56
0
Diagn
os
tic
f
or
St
ru
ctTS
Diag
nosti
c
plo
ts
f
or
Str
uct
TS
is
a
generic
functi
on
that
plo
ts
the
sta
ndar
diz
ed
resi
du
al
s
,
autoc
orrelat
ion
fu
ncti
on
of
th
e
residu
al
s
a
nd
p
-
val
ues
of
a
Po
rtm
anteau
te
st
fo
r
al
l
la
gs
in
dataset
s
hos
pital
bed
adm
issi
on
.
Ba
sed
on
the
diag
nosti
c
plo
t
s
f
or
e
ach
age
gro
up,
t
her
e
a
re
s
om
e
age
gro
ups
that
sho
w
th
e
sam
e
var
ia
ti
on
in
bed
a
dm
is
sion.
For
age
gro
up
s
le
ss
th
an
one
ye
ar
ol
d,
ther
e
is
huge
va
riat
ion
i
n
be
d
adm
issi
on
duri
ng
20
02
-
2005. H
owe
ver,
it
s
hows
the
sta
ble v
ariat
io
n
un
ti
l 201
4.
Th
e
sam
e
patte
r
n
is
al
s
o
se
e
n
for
se
ver
al
a
ge gr
oups exce
pt
for (3
5
-
44)
, (4
5
-
54), (
55
-
64) a
nd ag
e
m
or
e than 7
5
ye
a
rs old.
Fo
r
a
ge
group
of
(
35
-
44),
(
45
-
54)
a
nd
(55
-
64)
ye
ar
s
old
,
it
sh
ows
t
he
di
ff
e
ren
t
var
ia
ti
on
from
the
diag
nosti
c
plo
t
s.
The
patte
r
n
sh
ows
t
he
hi
gh
va
riat
ion
at
2001
an
d
tu
r
n
to
sm
all
var
ia
ti
on
to
wa
rd
s
t
he
la
te
r
ye
ars.
Fi
gure
3 sh
ows the
d
ia
gnos
ti
c
plo
ts
f
or these a
ge g
r
oups
:
Figure
3. Dia
gnos
ti
c
Plots
for
A
ge
(35
-
44)
, (45
-
54)
a
nd (5
5
-
64)
Yea
rs
Old
Fo
r
a
ge
group
s
of
(65
-
74)
a
nd
a
ge
m
or
e
than
75
ye
ars
old
,
t
he
sm
all
var
ia
ti
on
exist
s
at
the
early
ye
ars
an
d
tur
n
to
be
hi
gh
at
2006.
Howe
ver,
it
is
a
bit
sta
ble
up
unti
l
2015.
Dia
gnos
ti
c
plo
ts
f
or
fem
ale
age
gro
up
al
so
plot
te
d
in
or
de
r
to
see
the
diff
e
ren
ces
of
va
ria
ti
on
with
m
al
e
age
groups
.
Si
m
i
la
r
with
m
a
le
ag
e
gro
up
s
,
there
a
re
seve
ral
of
fe
m
al
e
age
groups
s
hows
the
s
a
m
e
var
ia
ti
on
. F
igure
4
show
s
the
diag
nosti
cs
plo
t
s
for
a
ge
le
ss
tha
n
on
e
ye
a
rs
old
an
d
this
var
ia
t
ion
al
s
o
sam
e
with
a
ge
gr
oups
20
-
24
an
d
25
-
34
ye
ars
ol
d.
Ther
e
is
s
m
all
var
ia
tio
n
in
bed
a
dm
i
ssio
n
durin
g
2001
an
d
cha
ng
es
to
huge
va
riat
ion
at
2002
-
2004
an
d
it
looks
big
sta
ble up
unti
l 201
2.
H
ow
e
ve
r,
it
s
hows
hu
ge
v
a
riat
ion
a
ga
in at 20
13 to
w
ard
s
the lat
er
yea
rs.
Fo
r
a
ge
gr
oup
1
-
4,
5
-
19
a
nd
55
-
64
ye
ars
old
,
the
patte
rn
s
hows
ver
y
sm
a
ll
var
ia
ti
on
at
2001
be
fore
tur
ning
int
o
huge
var
ia
ti
on
at
2002
-
2004
a
nd
looks
big
sta
bl
e
up
un
ti
l
20
11.
H
oweve
r,
t
he
re
is
huge
va
riat
ion
again
at
2012
towa
rds
the
l
at
er
ye
ars.
For
age
gro
up
35
-
44
a
nd
45
-
54
ye
ars
ol
d
the
patte
r
n
s
hows
high
var
ia
ti
on
in
20
01
unti
l
20
04
bef
or
e
t
urnin
g
to
sm
a
ll
var
ia
tio
n
t
ow
a
rds
the
la
te
r
ye
ars.
H
ow
e
ve
r,
it
sh
ows
the
huge
va
riat
ion
again
at
2014
towa
r
ds
the
la
te
r
ye
ars.
At
th
e
sa
m
e
t
i
m
e,
patte
rn
f
or
fem
al
e
age
group
of
(65
-
74)
a
nd a
ge
m
or
e
tha
n 75 ye
ars old a
re s
im
ilar wit
h
m
al
e g
r
oup wit
h sa
m
e
ages.
Evaluation Warning : The document was created with Spire.PDF for Python.
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci
IS
S
N:
25
02
-
4752
Alt
erna
ti
ve Me
thods f
or
F
or
e
castin
g
V
ar
iati
on
s
in
Hos
pital Bed
Ad
missio
n
(
S.
Sa
rif
ah
R
ad
i
ah Sh
ar
if
f
)
415
Figure
4. Dia
gnos
ti
c
Plots
for
A
ge
Les
s
tha
n
O
ne
, (
20
-
24
)
a
nd (2
5
-
34)
Yea
rs
Old
3.3 Per
fo
r
ma
nce Me
asure
s
To
eval
uate
the
per
f
or
m
ance
between
AR
I
MA
and
Stat
e
Sp
ace
Mo
del,
MSE
for
each
m
od
el
hav
e
been
cal
culat
e
d.
Inste
ad
of
f
urt
her
analy
zi
ng
the
da
ta
,
we
li
m
it
ou
r
a
naly
sis
on
fem
al
e
group
a
ge
betwe
en
25
-
34
only
.
T
his
i
s
due
t
o
the
hi
gh
e
st
va
riat
ion
show
n
by
t
he
gro
up.
F
or
eca
s
t
on
the
va
riat
ion
of
num
ber
of
be
d
adm
issi
on
a
m
on
g
fem
al
e
age
betwee
n
25
-
34
wer
e
done
by
con
str
uctin
g
the
m
od
el
based
o
n
data
per
i
od
of
2004
-
2014,
a
nd
com
par
in
g
f
or
ecast
values
for
data
pe
rio
d
of
20
15.
Tabl
e
4
show
s
the
com
par
ison
of
MSE
betwee
n
the
t
wo
m
od
el
s.
St
at
e
Sp
ace
m
od
el
ou
tpe
rfo
rm
s
ARIMA
due
to
it
s
lowest
MSE.
Th
us,
th
e
sta
te
sp
ace m
od
el
is
us
e
d
f
or fo
reca
sti
ng
pu
r
pose.
Table
4.
C
om
par
iso
n of M
SE
Mod
els
Valu
e of
M
SE
ARIMA
1
8
9
4
.8
3
State Space
8
3
4
.33
4.
CONCL
US
I
O
N
This
st
ud
y
a
na
ly
zes
the
va
r
ia
ti
on
s
in
num
ber
of
hosp
it
a
l
bed
a
dm
issio
n
bet
wee
n
a
ge
gro
up
s
of
diff
e
re
nt
gend
ers
us
in
g
AR
I
MA
and
Stat
e
Sp
ace
m
od
el
s.
The
find
i
ngs
from
the
stud
y
sh
ow
that
age
gr
ou
p
fem
al
e
of
25
-
34
ye
ars
old
ha
ve
the
highest
values
va
riat
ion
of
total
ho
s
pi
ta
l
bed
a
dm
issio
n.
F
ro
m
the
r
esults,
fem
al
e
with
age
within
25
unti
l
34
ye
ars
ol
d
are
m
or
e
unpredict
able
f
or
th
ei
r
healt
h.
It
see
m
s
true
beca
use
if
we
c
om
par
e
be
tween
m
al
e
and
fem
al
e,
the
la
tt
er
al
ways
f
ace
or
e
xp
e
rience
ph
ysi
cal
s
ym
pto
m
s
wh
ic
h
occur
m
uch
le
ss
f
re
qu
e
ntly
in
m
ale
beca
us
e
of
t
he
norm
al
patte
rn
s
of
fluct
ua
ti
on
durin
g
th
ei
r
m
enstru
al
cy
cl
e.
Re
la
te
d
with
age
of
25
unti
l
34
ye
ars
ol
d,
w
he
n
per
s
on
gro
ws
up
to
30
ye
ars
old
above,
their
body
is
changin
g
bit
by
bit
and
these
changes
are
a
norm
al
par
t
of
grow
i
ng
old
e
r.
W
he
n
pe
rs
on
is
reach
to
pr
i
m
e
age
of
40
a
nd
a
bove
,
we
can
ass
um
e
they
can h
a
ve
diseases bec
ause o
f
age
fac
tors.
But fo
r
pe
rson
with
a
ge
25
-
34
ye
ars
old
,
we
cannot
assum
e
or
pr
e
dict
generall
y
they
wil
l
hav
e
disease
s
or
not
because
it
dep
end
s
on
the
ind
ivi
du
al
li
fe
s
ty
le
.
Each
per
s
on
ha
s
diff
e
re
nt
li
festy
le
fro
m
their
nutrit
ion,
diets,
e
xerci
se
an
d
m
any
oth
e
rs,
so
it
d
epe
nds
on the p
e
rs
on
it
s
el
f
wh
et
her
eas
y t
o
get d
ise
as
es o
r no
t.
Gen
e
rall
y, wh
e
n
w
om
en
reach
to a
ge
30
above,
t
heir
m
et
abo
li
sm
becam
e
slow
an
d
bone
lo
ss
be
gi
ns
at
this
age
,
le
ad
to
the
bone
-
thi
nn
i
ng
di
sease
known
as
os
te
oporosis
la
te
r
i
n
li
fe.
T
he
un
healt
hy
nu
tr
it
i
on
al
facto
rs
al
so
le
a
d
t
o
the
diseases
su
c
h
as
hi
gh
blood p
ress
ur
e
,
h
ig
h
c
hole
ste
r
ol, breast
disea
ses and m
any ot
her
s.
In a
Stat
e Sp
ace
m
od
el
, th
e
var
ia
ti
on
wh
ic
h
sh
ows
the
hi
ghly
var
ie
d
is
sel
ect
ed
to
be
us
e
d
i
n
the
nex
t
f
or
ecast
in
g
pro
cess.
In
case
of
total
be
d
a
dm
issi
on
for
t
his
stu
dy, ag
e
gro
up
2
5
-
34
ye
ars
old
sho
ws
the
highest
var
ia
ti
on
wh
ic
h
m
eans
that
total
of
bed
adm
i
ssio
n
for
this
gro
up
is
unpredict
abl
e.
Th
e
f
or
e
cas
te
d
va
riat
ion
r
esults
f
ro
m
the
m
od
el
produ
ce
the
re
su
lt
s
wh
ic
h
appr
ox
im
at
e o
r
sim
il
ar to
the
act
ual v
a
riat
ion
from
d
at
aset
o
f
total
b
e
d
a
dm
issi
on
.
Howe
ver,
the
adm
issi
on
of
pa
ti
ents
into
a
hosp
it
al
is
not
ne
cessaril
y
du
e
to
il
lness,
it
can
be
due
to
giv
in
g
birth
a
nd
othe
r
rea
son
s.
He
nce,
m
or
e
researc
h
that
consi
der
oth
e
r
factors
an
d
ot
he
r
releva
nt
m
eth
ods
[12] that a
ff
ect
the a
dm
issi
on
into
a
hos
pital
sh
oul
d be
done
.
Evaluation Warning : The document was created with Spire.PDF for Python.
IS
S
N
:
2502
-
4752
Ind
on
esi
a
n
J
E
le
c Eng &
Co
m
p
Sci,
Vol
.
9
,
No.
2
,
Fe
br
uary
201
8
:
410
–
416
416
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