T
E
L
KO
M
NIK
A
, V
ol
.
17
,
No.
6,
Dec
em
be
r
20
1
9,
p
p.3
1
0
0~
3
1
0
9
IS
S
N: 1
69
3
-
6
93
0
,
accr
ed
ited
F
irst
Gr
ad
e b
y K
em
en
r
istekdikti,
Decr
ee
No: 2
1/E/
K
P
T
/20
18
DOI:
10.12928/TE
LK
OM
N
IK
A
.v
1
7
i
6
.
12729
◼
31
00
Rec
ei
v
ed
M
arc
h
23
,
20
1
9
;
Rev
i
s
ed
J
u
l
y
2
,
20
1
9
;
A
c
c
ep
ted
J
u
l
y
18
, 2
0
1
9
A
n
o
v
e
l m
od
el
f
or solar r
a
diat
i
o
n p
red
icti
on
Ibrahim
S
. M
adu
g
u
*1
, B. J
.
O
luf
ea
g
b
a
2
, Y
inu
sa
A
.
A
d
edira
n
3
,
F.
A
b
d
u
lk
adir
4
,
A
.
A
b
d
u
lka
r
im
5
,
Ja
m
es
. U
. Inaku
6
,
A
.
U. L
aw
an
7
1*
Dep
a
rtm
e
n
t
o
f
El
e
c
tri
c
a
l
En
g
i
n
e
e
ri
n
g
;
Ka
n
o
Un
i
v
e
rs
i
ty
o
f
Sc
i
e
n
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
W
u
d
i
l
,
Nig
e
ri
a
2
,
3,
6
Dep
a
r
tm
e
n
t
o
f
El
e
c
tri
c
a
l
a
n
d
El
e
c
tro
n
i
c
s
En
g
i
n
e
e
ri
n
g
,
Uni
v
e
rs
i
ty
o
f
I
l
o
ri
n
,
Nig
e
ri
a
4
Dep
a
rt
m
e
n
t
o
f
Che
m
i
s
try
Ed
u
c
a
ti
o
n
,
Ka
n
o
Un
i
v
e
rs
i
ty
o
f
Sc
i
e
n
c
e
a
n
d
T
e
c
h
n
o
l
o
g
y
,
W
u
d
i
l
,
Ni
g
e
ri
a
5
Dep
a
rt
m
e
n
t
o
f
El
e
c
tr
i
c
a
l
En
g
i
n
e
e
ri
n
g
,
Ah
m
a
d
u
Be
l
l
o
Un
i
v
e
r
s
i
ty
Z
a
ri
a
,
Ni
g
e
ri
a
7
Dep
a
rt
m
e
n
t
o
f
El
e
c
tr
i
c
a
l
En
g
i
n
e
e
ri
n
g
,
Hu
s
s
a
i
n
i
Ad
a
m
u
F
e
d
e
ra
l
Po
l
y
te
c
h
n
i
c
,
Ka
z
a
u
re
,
Nig
e
ri
a
*C
o
rre
s
p
o
n
d
i
n
g
a
u
th
o
r,
e
-
m
a
i
l
:
m
a
d
u
g
u
e
m
i
r@g
m
a
i
l
.
c
o
m
,
m
a
d
u
g
u
e
m
i
r@
k
u
s
tw
u
d
i
l
.e
d
u
.n
g
Ab
strac
t
En
e
rg
y
f
o
r
fu
l
f
i
l
l
i
n
g
b
a
s
i
c
c
o
m
m
u
n
i
ty
/
i
n
d
i
v
i
d
u
a
l
n
e
e
d
s
h
a
s
c
o
m
e
to
c
o
n
s
ti
t
u
te
th
e
fi
rs
t
a
rti
c
l
e
o
f
e
x
p
e
c
ta
t
i
o
n
i
n
a
l
l
c
o
n
t
e
m
p
o
r
a
ry
s
o
c
i
e
ti
e
s
.
T
h
e
e
x
p
l
o
i
t
a
ti
o
n
o
f
re
n
e
wab
l
e
s
n
o
ta
b
l
y
s
o
l
a
r
i
n
e
l
e
c
tri
c
i
ty
g
e
n
e
ra
ti
o
n
h
a
s
b
ro
u
g
h
t
re
l
i
e
f
to
th
e
f
u
l
f
i
l
m
e
n
t
o
f
e
n
e
rg
y
d
e
m
a
n
d
e
s
p
e
c
i
a
l
l
y
a
m
o
n
g
s
u
s
c
e
p
ti
b
l
e
c
o
m
m
u
n
i
ti
e
s
.
In
th
i
s
p
a
p
e
r y
e
a
rl
y
m
i
n
i
m
u
m
s
o
l
a
r ra
d
i
a
ti
o
n
o
f
Ka
n
o
(1
2
.
0
5
°N; 0
8
.2
°E;
a
l
ti
tu
d
e
4
7
2
.5
m
;
3
a
i
r
d
e
n
s
i
ty
1
.1
7
0
5
k
g
/m
3
)
fo
r
4
6
y
e
a
r
s
i
s
u
s
e
d
to
g
e
n
e
r
a
te
a
p
re
d
i
c
ti
o
n
m
o
d
e
l
th
a
t
fi
t
s
th
e
d
a
t
a
u
s
i
n
g
a
u
to
re
g
re
s
s
i
v
e
m
o
v
i
n
g
a
v
e
r
a
g
e
(ARM
A)
a
n
d
a
n
e
w
m
o
d
e
l
te
rm
e
d
a
u
to
re
g
re
s
s
i
v
e
m
o
v
i
n
g
a
v
e
ra
g
e
p
ro
c
e
s
s
(AR
M
AP).
Com
p
a
ri
s
o
n
b
e
twe
e
n
t
h
e
ARM
A a
n
d
AR
M
AP
m
o
d
e
l
s
s
h
o
we
d
a
t
re
m
e
n
d
o
u
s
i
m
p
ro
v
e
i
n
t
h
e
s
u
m
o
f
s
q
u
a
re
e
rro
r r
e
d
u
c
ti
o
n
b
e
twe
e
n
t
h
e
a
c
tu
a
l
d
a
ta
a
n
d
t
h
e
f
o
r
e
c
a
s
te
d
d
a
ta
b
y
4
7
%
.
Key
w
ords
:
m
e
a
n
a
b
s
o
l
u
te
p
e
rc
e
n
t
a
g
e
e
rro
r,
s
o
l
a
r
r
a
d
i
a
ti
o
n
,
s
u
m
o
f
s
q
u
a
re
e
rro
r
,
ro
o
t
m
e
a
n
s
q
u
a
r
e
e
rr
o
r,
ti
m
e
s
e
r
i
e
s
Copy
righ
t
©
2
0
1
9
Uni
v
e
rsi
t
a
s
Ahm
a
d
D
a
hl
a
n.
All
rig
ht
s
r
e
s
e
rve
d
.
1.
Int
r
o
d
u
ctio
n
A
l
t
ho
u
gh
e
l
ec
tr
i
c
a
l
en
erg
y
i
s
s
el
do
m
av
a
i
l
ab
l
e
as
a
p
r
i
m
ary
f
orm
,
i
t
i
s
m
os
t
c
o
m
m
on
l
y
us
ed
i
n
m
od
ern
l
i
v
i
ng
.
T
hi
s
i
s
be
c
au
s
e
i
t
i
s
ea
s
y
to
tr
a
ns
po
r
t
be
t
w
ee
n
d
i
s
tan
t
l
oc
ati
o
ns
an
d
c
an
ef
f
i
c
i
en
tl
y
b
e
us
ed
to
pro
v
i
de
ne
e
de
d
p
o
w
er
to
pe
r
f
orm
v
ario
us
f
un
c
ti
on
s
t
ha
t
m
ak
e
ex
i
s
ten
c
e
be
ara
bl
e
[1]
.
E
n
erg
y
de
m
an
d
i
n
t
he
W
orld
an
d
i
n
Ni
ge
r
i
a
h
as
ex
pe
r
i
en
c
e
d
a
tr
em
en
do
us
i
nc
r
ea
s
e
as
h
um
an
ac
ti
v
i
ti
es
are
m
ad
e
m
ore
c
on
v
e
ni
e
nt
thro
ug
h
t
he
us
e
of
el
ec
tr
on
i
c
s
an
d
el
ec
tr
i
c
a
l
de
v
i
c
es
(
Com
pu
ter,
ph
on
es
,
el
ec
tr
i
c
k
ett
l
e,
was
hi
n
g
m
ac
hi
ne
an
d
s
o
o
n).
T
hi
s
de
m
an
d
i
s
proj
ec
te
d
t
o
tr
i
pl
e
b
y
th
e
y
ea
r
20
50
[2]
.
L
i
k
el
y
ac
erbati
ng
th
e
a
l
r
ea
d
y
s
erio
us
gree
nh
o
us
e
ef
f
ec
t
att
r
i
bu
te
d
t
o
t
he
m
as
s
i
v
e
c
on
s
um
pti
on
of
en
erg
y
pro
v
i
de
d
b
y
f
os
s
i
l
f
u
el
i
n
the
l
as
t
c
en
tur
y
[3]
.
Co
ns
eq
u
en
t
l
y
,
a
s
erio
us
r
ed
uc
ti
o
n
i
n
f
os
s
i
l
-
f
ue
l
p
o
w
er
s
o
urc
es
m
us
t
oc
c
ur
i
m
pl
y
i
n
g
tha
t re
ne
w
a
bl
e e
ne
r
g
y
m
us
t b
ec
om
e d
om
i
na
nt
[4
,
5]
.
Ni
ge
r
i
a
ha
s
a
hu
g
e
s
ol
ar
en
erg
y
po
t
en
t
i
al
r
an
g
i
ng
b
et
w
e
en
1,8
0
0
K
W
h/
m
2
to
the
S
o
uth
ern
r
e
gi
on
an
d
m
ore
tha
n
2,
30
0
K
W
h/m
2
to
the
Nor
th
ern
r
eg
i
o
n
as
s
ho
w
n
i
n
F
i
gu
r
e
1
[6
,
7]
.
T
he
ab
u
nd
an
c
e
of
s
ol
ar
en
erg
y
i
n
Ni
g
eria
i
s
h
ug
e
,
the
r
ad
i
ate
d
s
un
’
s
e
ne
r
g
y
i
s
ab
ou
t
3.8
x
10
23
K
W
w
hi
c
h
i
s
1.0
8
2
m
i
l
l
i
o
n
t
on
n
es
of
oi
l
e
qu
i
v
al
en
t
(
m
toe
)
.
T
hi
s
s
ol
ar
po
te
nti
al
i
s
m
ore
tha
n
4
00
0
t
i
m
es
an
d
13
00
0
t
i
m
es
of
Ni
ge
r
i
a
da
i
l
y
pr
od
uc
t
i
on
of
c
r
ud
e
o
i
l
a
nd
na
tura
l
ga
s
r
es
pe
c
ti
v
el
y
[8
,
9]
.
T
he
r
e
i
s
n
ee
d
t
o
ha
r
ne
s
s
r
en
e
wab
l
e
en
erg
y
(
R
E
)
s
ou
r
c
es
s
uc
h
as
s
o
l
ar
en
e
r
g
y
i
n
de
v
el
op
i
ng
c
ou
ntr
i
es
l
i
k
e
Ni
ge
r
i
a
f
or
s
us
ta
i
na
bl
e
e
n
erg
y
pro
v
i
s
i
on
to
brin
g
a
b
ou
t
ec
on
om
i
c
de
v
el
op
m
en
t,
r
ural
de
v
e
l
o
p
m
en
t,
ea
s
e
of
l
i
v
i
ng
an
d
pr
ov
i
de
c
l
ea
n
e
ne
r
g
y
f
r
om
th
e
pe
r
s
pe
c
t
i
v
e
of
the
K
y
oto
ag
r
e
em
en
t.
It
i
s
i
m
pe
r
ati
v
e
to
n
ote
t
ha
t
on
l
y
a
bo
ut
40
%
of
the
tot
a
l
po
pu
l
ati
on
i
n
Ni
ge
r
i
a
ha
v
e
ac
c
es
s
to
e
l
ec
tr
i
c
i
t
y
,
o
ut
of
w
h
i
c
h o
nl
y
ab
ou
t 5
% of
th
e
r
ural
are
as
ar
e p
r
i
v
y
to
s
uc
h
el
ec
tr
i
c
i
t
y
[10
,
11]
.
T
he
c
om
m
un
i
ti
es
wi
th
t
he
ac
c
es
s
ha
r
dl
y
e
nj
o
y
m
ore
tha
n
48
ho
urs
pe
r
week
of
un
i
nt
err
up
t
i
b
l
e
p
o
w
er
s
up
pl
y
d
ue
to
s
o
m
an
y
probl
em
s
f
r
o
m
the
ge
ne
r
a
ti
o
n
d
o
w
n
to
di
s
tr
i
b
uti
on
[
12
]
.
Re
ga
r
d
i
n
g
the
s
e
,
M
i
c
r
og
r
i
d
(
es
pe
c
i
al
l
y
s
o
l
ar)
m
i
gh
t
b
e
us
ed
to
m
i
ti
ga
te
the
prob
l
em
[8]
.
S
o
l
ar
ph
oto
v
ol
tai
c
tec
hn
ol
og
y
ha
s
nu
m
erous
ad
v
an
t
ag
es
,
s
i
n
c
e
i
t
r
ed
uc
es
green
ho
us
e
ef
f
ec
t
[13
,
14
]
,
c
an
be
i
ns
tal
l
ed
i
n
a
m
od
ul
ar,
qu
i
c
k
l
y
i
nc
r
ea
s
e
ge
ne
r
ati
on
e
v
e
n
t
o
r
em
ote
s
t c
o
m
m
un
i
t
y
an
d
c
an
e
as
i
l
y
b
e f
un
de
d b
y
i
nd
i
v
i
du
a
l
s
or c
oo
pe
r
at
i
v
es
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
no
v
e
l
mo
d
el
f
or s
ol
ar r
ad
i
ati
o
n p
r
e
di
c
t
i
on
(
I
brah
i
m
S
.
Ma
du
gu
)
3101
S
ol
ar
e
ne
r
g
y
c
o
nv
ers
i
on
r
e
qu
i
r
es
the
k
no
wl
ed
ge
of
th
e
s
ol
ar
r
ad
i
at
i
o
n
d
ata
of
th
e
are
a
of
ap
pl
i
c
ati
on
as
i
t
i
s
no
t
gl
ob
a
l
l
y
un
i
f
orm
[1
-
15]
.
T
he
av
a
i
l
ab
i
l
i
t
y
of
the
em
pi
r
i
c
al
da
ta
m
ak
es
i
t
f
ea
s
i
bl
e
to
c
r
ea
t
e
a
m
od
el
us
i
ng
v
ar
i
ou
s
t
ec
hn
i
qu
es
.
Ho
w
e
v
er,
i
f
the
d
ata
i
s
l
ac
k
i
ng
th
en
t
he
us
e
of
em
pi
r
i
c
al
e
qu
at
i
o
ns
of
areas
wi
th
al
m
os
t
s
i
m
i
l
ar
c
l
i
m
ate
c
an
be
d
ep
l
o
y
ed
[16]
.
E
l
ec
tr
i
c
po
w
er
g
en
era
ti
o
n
i
n
Ni
ge
r
i
a
f
ac
es
nu
m
erous
c
ha
l
l
en
g
es
an
d
th
e
i
nc
r
ea
s
e
i
n
the
pric
e
of
oi
l
i
n
the
m
i
d
-
19
70
s
tha
t
ac
c
om
pa
ni
ed
pros
pe
r
i
t
y
tr
i
gg
ered
a
ph
en
om
en
al
of
grow
t
h
i
n
e
l
ec
tr
i
c
a
l
ap
p
l
i
a
nc
es
f
or
s
oc
i
al
,
c
o
m
m
erc
i
al
an
d
i
nd
us
tr
i
al
u
s
e
[8]
.
W
hi
l
e
s
uc
h
i
nc
r
ea
s
e
i
n
de
m
an
d
oc
c
urr
ed
al
m
os
t
i
m
m
ed
i
ate
l
y
,
t
he
p
o
w
er
to
op
era
te
th
em
c
ou
l
d
n
ot
k
ee
p
pa
c
e.
T
he
r
es
ul
t
was
a
po
wer
gr
i
d
wi
t
h
p
erf
or
m
an
c
e
pr
og
r
es
s
i
v
el
y
de
g
en
erated
an
d
h
as
r
es
i
s
te
d
a
l
l
att
em
pts
to
r
ev
ers
e t
he
tre
nd
.
T
he
s
toc
ha
s
ti
c
na
ture
of
r
en
e
wabl
es
l
i
k
e
s
ol
ar
r
a
di
a
t
i
on
i
s
i
ts
m
aj
or
draw
b
ac
k
as
i
t
i
s
di
f
f
i
c
ul
t
to
ea
s
i
l
y
f
orm
ul
ate
a
pre
di
c
t
i
on
m
od
el
[1
7]
.
Ho
w
e
v
er,
t
he
us
e
of
s
tat
i
s
ti
c
al
ap
proac
h
s
uc
h
as
ti
m
e
s
erie
s
B
ox
a
nd
J
en
k
i
ns
proc
ed
ur
e
[16
]
A
RM
A
m
a
k
es
i
t
po
s
s
i
bl
e
t
o
es
ti
m
ate
an
d
f
orec
as
t
the
ne
x
t
ge
ne
r
at
i
o
n
of
s
ol
ar
r
ad
i
a
ti
o
n
da
ta
[1
8]
.
O
ne
of
the
s
ho
r
tc
om
i
ng
s
of
predi
c
ti
on
wi
th
A
R
MA
i
s
th
at
i
t
r
e
qu
i
r
es
m
an
y
da
t
a
p
oi
nts
f
or
be
tt
er
ac
c
urac
y
an
d
th
e
da
ta
m
us
t
be
s
tat
i
o
na
r
y
[1]
.
T
he
m
en
ti
o
ne
d
s
h
ortc
om
i
ng
s
of
A
RM
A
m
oti
v
a
ted
the
d
ev
el
o
pm
en
t
of
a
n
ov
el
h
y
br
i
d t
i
m
e
s
erie
s
m
od
el
te
r
m
ed
A
RM
A
P
.
F
i
gu
r
e
1.
M
ap
of
Ni
ge
r
i
a s
o
l
ar en
erg
y
po
ten
t
i
a
l
2.
A
RM
A
M
o
d
el
T
he
s
ol
ar
r
ad
i
at
i
o
n
t
i
m
e
s
erie
s
i
s
c
om
po
s
ed
of
a
s
eq
u
en
c
e
of
d
ai
l
y
s
ol
ar
i
ns
ol
a
ti
o
n
o
v
er
the
pe
r
i
od
of
46
y
e
ars
b
et
ween
19
71
an
d
2
01
6
o
bs
e
r
v
ati
on
s
{
y
t
}
.
A
c
om
m
on
l
y
u
s
ed
a
v
e
nu
e
f
or
ti
m
e
s
erie
s
predi
c
ti
on
i
s
the
au
tore
gres
s
i
v
e
m
ov
i
ng
a
v
erag
e
(
A
RM
A
)
m
od
el
s
aft
er
en
es
uri
ng
tha
t
t
he
t
i
m
e
s
erie
s
i
s
s
tat
i
on
ar
y
[
19
]
.
A
R
MA
ha
s
t
he
c
ap
ab
i
l
i
t
y
of
ex
tr
ac
ti
ng
us
ef
ul
s
tat
i
s
t
i
c
al
propert
i
es
us
i
ng
the
w
e
l
l
k
no
w
n
B
ox
a
nd
J
e
nk
i
ns
m
od
el
[20]
.
T
he
ge
ne
r
a
l
A
uto
r
eg
r
es
s
i
v
e
Mo
v
i
n
g A
v
er
ag
e,
A
R
MA
(
p,
q
)
f
or a s
ol
ar r
ad
i
at
i
o
n
,
is
g
i
v
en
b
y
:
=
∑
=
1
−
+
∑
ℎ
ℎ
=
1
−
ℎ
+
(
1)
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
31
0
0
-
31
0
9
3102
where
,
are
c
o
ef
f
i
c
i
en
ts
of
A
R
an
d
M
A
r
es
pe
c
ti
v
e
l
y
;
i
s
a
r
a
nd
om
proc
es
s
w
i
t
h
z
ero
m
ea
n
an
d
c
on
s
tan
t
v
ari
an
c
e.
T
he
B
ox
-
J
en
k
i
ns
proc
ed
ure
i
s
ba
s
ed
o
n
3
p
i
l
l
ars
[
20
,
2
1]
as
s
ho
w
n
i
n
F
i
gu
r
e
2.
F
i
gu
r
e
2.
B
ox
an
d J
en
k
i
ns
A
RM
A
m
eth
od
o
l
og
y
2.1
. M
o
d
el
Iden
t
if
ica
t
ion
T
he
A
uto
c
orr
el
ati
on
F
un
c
t
i
on
(
A
CF
)
an
d
P
art
i
al
A
ut
o
c
orr
el
ati
on
F
un
c
t
i
o
n
(
P
A
C
F
)
pl
ots
are
c
om
pa
r
ed
wi
th
t
he
th
e
oreti
c
a
l
c
ata
l
og
t
o
i
de
nt
i
f
y
m
od
el
.
A
pu
r
e
au
tor
eg
r
es
s
i
v
e
wi
l
l
ha
v
e
i
t
s
A
CF
s
pi
k
es
de
c
a
y
i
n
g
to
wa
r
ds
z
ero
a
nd
t
he
P
A
CF
c
ut
s
-
off
af
ter
the
p
l
a
g(s
)
.
W
hi
l
e
th
e
m
ov
i
n
g
av
era
ge
i
s
o
po
s
i
t
e
of
au
tor
eg
r
es
s
i
v
e
w
h
i
l
e
t
he
A
RM
A
m
od
el
ha
v
e
ge
om
etri
c
al
d
ec
a
y
f
or
b
oth
A
CF
a
nd
P
A
CF
.T
he
l
ag
s
̂
(
)
a
r
e d
ef
i
ne
d a
s
:
ρ
̂
(
k
)
=
∑
(
y
t
−
μ
)
n
−
k
t
=
1
(
y
t
+
k
−
μ
)
∑
(
y
t
−
μ
)
2
n
t
=
1
(
2)
where
k
i
s
t
he
nu
m
be
r
of
l
a
gs
an
d
i
s
th
e m
ea
n o
f
th
e
s
ol
ar r
ad
i
at
i
on
da
t
a,
.
T
he
pa
r
ti
a
l
au
t
oc
orr
el
at
i
o
n
f
un
c
ti
on
(
P
A
CF
)
,
i
s
a
r
e
pres
en
tat
i
o
n
of
th
e
c
orr
e
l
a
ti
on
be
t
w
e
en
the
d
ev
i
at
i
o
ns
i
n
the
da
t
a
a
nd
the
l
i
n
ea
r
r
e
l
ati
o
n
f
r
om
the
i
nte
r
m
ed
i
at
e
v
aria
bl
es
i
n
the
p
arti
a
l
a
uto
c
orr
e
l
at
i
on
f
un
c
ti
on
wi
th
k
th
pa
r
ti
al
c
orr
el
ati
on
c
o
ee
f
i
c
i
e
nt.
T
he
P
A
CF
i
s
de
f
i
ne
d
as
:
ϕ
kk
=
ρ
̂
(
k
)
−
∑
α
k
−
1
,
j
ρ
̂
k
−
j
k
−
1
j
=
1
1
−
∑
α
k
−
1
,
j
ρ
̂
j
k
−
1
j
=
1
(
3)
ϕ
k
,
j
=
ϕ
k
−
1
,
j
−
ϕ
kk
ϕ
k
−
1
,
k
−
j
j
=
1
,
2
,
…
,
k
−
1
(
4)
T
he
s
pi
k
es
i
n
the
A
CF
a
nd
P
A
CF
gi
v
e
gu
i
da
nc
e
to
the
na
ture
of
the
m
od
el
pa
r
am
ete
r
s
.
A
n
A
CF
tha
t
di
es
do
wn
ex
po
ne
nti
al
l
y
an
d
P
A
CF
tha
t
ha
s
s
pi
k
es
i
n
l
a
gs
,
p
i
s
s
ai
d
to
be
pu
r
e
l
y
A
RM
A
(
p,0)
.
W
hi
l
e
th
e
o
p
po
s
i
te
of
A
R
proc
es
s
es
i
nd
i
c
at
es
m
ov
i
n
g
a
v
er
ag
e
(
MA
)
proc
es
s
.
T
he
A
RMA
(
p,
q
)
ha
s
bo
t
h
A
CF
an
d
P
A
CF
s
pi
k
es
de
c
ay
to
w
ar
ds
z
ero.
O
nc
e
t
he
A
CF
an
d
P
A
CF
wer
e
i
de
n
ti
f
i
e
d
th
e
m
od
el
pa
r
am
ete
r
s
nu
m
be
r
are
s
pe
c
ul
ate
d
an
d
s
e
v
era
l
m
od
el
s
are
us
e
d
whereof
th
e
m
os
t p
ars
i
m
on
i
ou
s
m
od
el
i
s
c
ho
s
en
.
2.2
.
P
a
r
amet
e
r
E
stim
atio
n
T
hi
s
i
nv
o
l
v
es
the
s
e
l
ec
t
i
on
of
pa
r
am
ete
r
s
(
p,q)
ba
s
ed
o
n
the
be
h
av
i
o
ur
of
the
au
t
oc
orr
el
a
ti
o
n
f
un
c
t
i
o
n
(
A
CF
)
an
d
pa
r
t
i
al
a
uto
c
orr
el
ati
on
f
un
c
ti
o
n
(
P
A
C
F
)
.
T
he
r
e
are
v
ari
ou
s
m
eth
od
s
of
es
t
i
m
a
tes
s
uc
h
as
Y
u
l
e
-
W
al
k
er,
l
ea
s
t
s
qu
are,
m
ax
i
m
u
m
l
i
k
el
i
h
oo
d
a
nd
s
o
on
.
T
he
l
ea
s
t
-
s
qu
are
m
eth
od
i
s
us
ed
t
o
f
i
nd
th
e
c
oe
f
f
i
c
i
en
t(
s
)
of
the
pa
r
am
ete
r
of
an
au
tore
gres
s
i
v
e m
od
el
. For
A
R(
1) th
e l
e
as
t s
qu
are es
t
i
m
ate
i
s
gi
v
en
b
y
:
α
1
=
∑
(
y
t
−
y
t
−
1
)
2
N
t
=
1
∑
y
t
2
N
t
=
1
(
5)
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
no
v
e
l
mo
d
el
f
or s
ol
ar r
ad
i
ati
o
n p
r
e
di
c
t
i
on
(
I
brah
i
m
S
.
Ma
du
gu
)
3103
Cons
i
d
erin
g
A
R(
n)
w
h
ere n
>
1,
t
he
n
w
e
ha
v
e:
(
α
1
α
2
⋮
α
n
)
=
(
a
11
a
12
…
a
1m
a
21
a
22
…
a
2m
⋮
a
n1
⋮
…
⋮
…
⋮
a
nm
)
−
1
(
b
1
b
2
⋮
b
k
)
(
6)
where
=
a
nn
=
∑
(
y
t
−
n
)
2
N
t
=
1
(
7)
f
or
≠
a
nm
=
a
mn
=
∑
(
y
t
−
n
−
y
t
−
m
)
2
N
t
=
1
(
8)
b
k
=
∑
(
y
t
−
y
t
−
k
)
2
N
t
=
1
(
9)
where
y
t
i
s
th
e
ac
tua
l
d
ata
.
2.3
. M
o
d
el
Diagn
o
stic Ch
ec
king
S
e
v
era
l
A
R
MA
m
od
el
s
w
er
e
c
om
pu
ted
us
i
ng
the
s
am
e
ti
m
e
s
erie
s
da
ta,
bu
t
t
he
m
os
t
pa
r
s
i
m
on
i
ou
s
(
a
de
q
ua
te)
i
s
c
ho
s
en
as
th
e
b
es
t
f
or
the
da
ta.
T
he
r
e
are
v
ari
ou
s
w
a
y
s
of
di
a
gn
os
t
i
c
c
he
c
k
i
ng
of
A
R
MA
m
od
el
,
bu
t
a
l
l
are
ba
s
e
d
on
the
r
es
i
d
ua
l
s
.
T
he
f
ol
l
o
w
i
n
g
g
oo
d
n
es
s
of
f
i
t te
s
t
is
us
ed
t
o o
bta
i
n t
he
m
os
t a
de
qu
ate
m
od
el
:
-
T
he
ti
m
e
pl
ot
of
th
e
r
es
i
du
al
be
h
av
es
l
i
k
e
the
n
orm
al
di
s
tr
i
bu
t
i
o
n,
wi
th
a
pp
r
ox
i
m
ate
l
y
z
er
o
m
ea
n a
nd
c
on
s
ta
nt
v
ari
an
c
e.
-
S
pi
k
es
of
the
pl
o
ts
of
r
es
i
du
al
s
A
CF
an
d
P
A
CF
s
ho
u
l
d
l
i
e
w
i
t
hi
n
the
95
%
c
on
f
i
d
en
c
e
i
n
terv
al
(
CI)
bo
un
ds
. T
ha
t i
s
:
CI
(
b
ound
)
=
±
1
.
96
√
N
⁄
(
10
)
where
N
i
s
th
e s
am
pl
e d
at
a
s
i
z
e
(
no
t
l
es
s
th
a
n 2
5% of
the
t
ota
l
s
i
z
e o
f
th
e d
a
ta
s
i
z
e)
-
T
he
A
k
ai
k
e
Inf
or
m
ati
on
Cr
i
t
erio
n:
F
or
a
t
i
m
e
s
erie
s
of
l
en
gt
h
n,
the
l
o
wes
t
A
IC
g
i
v
es
the
be
s
t
an
d m
os
t p
ars
i
m
on
i
ou
s
m
od
el
.
A
IC
i
s
d
ef
i
ne
d
b
y
:
A
IC
=
n
×
ln
(
∑
e
n
t
=
1
2
n
)
+
2
(
p
+
q
)
(
11
)
where
e
2
i
s
the
d
i
f
f
erenc
e
be
t
w
ee
n
ac
tu
al
a
nd
f
orec
as
ted
v
al
u
e;
n
i
s
nu
m
be
r
of
ob
s
erv
ati
on
s
and
p
an
d
q
are m
od
el
ord
er
[20
-
2
2]
.
3.
P
r
o
p
o
se
d
A
u
t
o
r
egre
ss
i
v
e
M
o
v
ing
A
v
er
ag
e P
r
o
ce
ss
(
A
RM
A
P
)
M
o
d
el
T
he
ti
m
e
s
erie
s
A
RM
A
m
od
el
f
al
l
s
u
nd
er
t
he
tr
ad
i
ti
o
n
al
m
eth
od
of
f
orec
as
ti
ng
a
m
on
g
the
thre
e
oth
er
c
l
as
s
i
f
i
c
at
i
o
ns
of
f
orec
as
ti
ng
.
T
he
oth
er
m
eth
od
s
ha
v
e
be
en
ne
w
t
ec
hn
i
qu
es
an
d
bottom
-
up
ap
proac
h
es
.
T
he
h
y
bri
d
of
two
m
eth
od
s
of
f
orec
as
ti
ng
i
s
ex
pe
c
t
ed
to
greatl
y
i
m
prov
e
the
ac
c
urac
y
of
th
e f
orec
as
ti
ng
m
od
el
of
th
e s
o
l
ar r
a
di
ati
o
n.
A
m
od
el
term
ed
A
uto
r
e
gre
s
s
i
v
e
Mo
v
i
ng
A
v
er
ag
e
P
r
oc
es
s
(
A
RM
A
P
)
i
s
de
v
e
l
o
pe
d
us
i
ng
a
h
y
br
i
d
s
y
s
tem
ti
m
e
s
eri
es
i
nc
l
u
di
n
g
an
i
nt
eg
r
al
of
a
c
ertai
n
n
um
be
r
of
prec
ed
i
ng
v
al
ue
s
.
T
he
ne
w
m
od
el
,
A
R
MA
P
i
s
de
v
el
op
ed
ba
s
ed
o
n
t
he
pri
nc
i
p
l
e
of
Z
i
e
gl
er
-
Ni
c
ho
l
s
r
u
l
es
f
o
r
P
ID
c
on
tr
ol
l
er
tun
i
ng
,
w
he
r
e
the
pa
r
am
ete
r
s
of
th
e
P
ID
c
on
tr
o
l
l
ers
c
an
be
s
el
ec
ted
f
r
o
m
the
m
ath
em
ati
c
al
m
od
el
or
b
y
ex
p
erim
en
ts
of
the
p
l
a
nt
t
o
i
m
prov
e
i
ts
s
tab
i
l
i
t
y
(
tr
an
s
i
en
t
an
d
s
tea
d
y
-
s
ta
te).
T
he
A
RM
A
P
i
s
de
v
el
op
e
d
to
f
i
ne
tu
ne
the
A
RM
A
ti
m
e
s
erie
s
m
od
el
.
T
hi
s
i
s
ac
c
om
pl
i
s
he
d
b
y
i
ntrod
uc
i
ng
a
n
i
nt
eg
r
a
l
v
ari
ab
l
e
V
n
whi
c
h
i
s
a
dd
e
d
as
a
b
uf
f
er
be
twee
n
a
s
tat
i
on
ar
y
an
d
n
on
-
s
ta
ti
on
ar
y
ti
m
e
s
erie
s
.
It
h
as
a
l
en
gth
w
,
bo
un
d
ed
w
-
1<
w
>
w
/4
.
T
he
propo
s
ed
ne
w
m
od
el
i
s
de
f
i
ne
d
as
:
Y
t
=
∑
α
k
p
k
=
1
y
t
−
k
+
V
k
+
1
γ
+
∑
β
h
q
h
=
1
ε
t
−
h
+
ε
t
(1
2
)
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
31
0
0
-
31
0
9
3104
the
p
aram
ete
r
,
V
n
i
s
de
f
i
ne
d i
n
(
1
3
).
V
n
=
γ
2n
[
(
y
t
−
1
+
y
t
−
n
)
+
2
∑
y
t
−
k
n
−
1
k
=
2
]
(1
3
)
where
n
i
s
i
nte
ge
r
:
2
,3,
..
;
t
i
s
i
nte
ge
r
: 1
,
2,…
an
d
k
i
s
i
nt
eg
er: 2
,3,
…
.
A
l
s
o,
a s
erie
s
P
M
A
(
z
)
i
s
i
nc
l
u
de
d
,
w
h
ere th
e p
aram
ete
r
z
i
s
a
dd
e
d a
nd
d
ef
i
ne
d
as
:
z
=
{
p
p
>
q
q
q
>
p
(
14
)
where
p
an
d
q
ar
e
t
he
au
t
oregr
es
s
i
v
e
a
nd
m
ov
i
ng
av
erag
e
pa
r
am
ete
r
s
r
es
pe
c
ti
v
e
l
y
.
T
he
m
atri
c
es
of
th
e c
oe
f
f
i
c
i
en
ts
of
th
e
A
R
MA
P
p
aram
e
ter es
ti
m
ati
on
are f
ou
n
d a
s
f
ol
l
o
w
s
:
a
nn
=
∑
(
Y
t
−
n
)
2
N
t
=
1
(
15
)
f
or
≠
;
a
nm
=
a
mn
=
∑
(
Y
t
−
n
−
V
n
)
2
N
t
=
1
(
16
)
b
k
=
∑
(
Y
t
−
Y
t
−
k
)
2
N
t
=
1
(
17
)
where
, i
s
th
e s
ol
ar r
ad
i
at
i
o
n d
at
a.
4.
F
o
r
e
ca
stin
g
and
P
e
r
f
o
r
man
ce
of
A
RM
A
and
A
RM
A
P
T
he
v
erac
i
t
y
of
the
de
v
e
l
op
ed
m
od
el
i
s
tes
t
ed
b
y
pred
i
c
ti
ng
the
ne
x
t
ge
n
erat
i
on
of
s
ol
ar
r
ad
i
at
i
o
n
d
ata
us
i
ng
th
e
a
v
a
i
l
a
bl
e
da
ta,
w
he
r
e
M
S
-
E
x
c
el
i
s
us
ed
f
or
al
l
c
al
c
u
l
a
ti
on
s
an
d
da
t
a
f
i
tti
ng
.
A
c
c
urac
y
i
s
a
m
aj
or
f
un
da
m
en
tal
of
a
n
y
f
orec
as
ti
ng
m
od
el
.
W
hi
l
e
a
r
oo
t
m
ea
n
s
qu
are
err
or
(
RMS
E
)
of
l
es
s
th
an
20
%
i
s
s
i
gn
i
f
i
c
an
t
y
e
t
th
e
l
es
s
er
t
he
err
or
th
e
be
tt
er,
e
v
en
th
ou
g
h
an
o
v
er
f
i
tt
i
ng
s
ho
u
l
d
be
a
v
oi
d
ed
s
o
as
no
t
to
n
eg
ate
t
he
pri
nc
i
p
l
e
of
pa
r
s
i
m
on
y
.
Cons
i
d
er
(
)
i
s
the
ac
t
ua
l
da
t
a,
(
)
i
s
the
f
o
r
ec
as
ted
s
ol
ar
r
ad
i
ati
on
d
at
a
an
d
n
i
s
t
he
d
ata
s
i
z
e
.
T
he
v
ar
i
ou
s
pe
r
f
or
m
an
c
e i
nd
i
c
es
of
f
orec
as
ti
ng
m
od
el
s
c
on
s
i
de
r
e
d
i
n t
hi
s
w
ork
are:
U
=
[
∑
(
(
A
(
t
)
−
F
(
t
)
)
2
n
)
n
t
=
1
]
1
/
2
[
∑
A
(
t
)
2
n
n
t
=
1
]
1
/
2
∗
[
∑
F
(
t
)
2
n
n
t
=
1
]
1
/
2
(
18
)
R
M
SE
=
(
1
n
√
∑
(
A
(
t
)
−
F
(
t
)
)
2
n
t
=
1
)
×
100
(
19
)
M
A
PE
=
1
n
∑
|
A
(
t
)
−
F
(
t
)
|
n
t
−
1
(
20
)
SSE
=
∑
(
A
(
t
)
−
F
(
t
)
)
2
n
t
−
1
(
21
)
where
U
i
s
T
he
i
l
’
s
U
-
s
tat
i
s
ti
c
,
RM
S
E
i
s
Ro
ot
M
ea
n
S
qu
are
E
r
r
or,
M
A
P
E
i
s
Me
an
A
bs
ol
u
te
P
erc
en
t
ag
e
E
r
r
or an
d
S
S
E
i
s
S
um
of
S
qu
are
E
r
r
or
[2
3
-
25]
.
5.
R
es
u
lt
s
and
Dis
cussi
o
n
5.1
.
S
o
la
r
Radi
atio
n
Data
T
he
46
y
e
ars
(
1
st
J
a
nu
ar
y
,
19
7
1
to
31
st
Dec
em
be
r
,
20
16
)
da
i
l
y
m
ea
n
s
ol
ar
r
a
di
at
i
o
n
da
ta
(
MJ
/m
2
/da
y
)
w
ere
c
ol
l
ec
ted
f
r
om
the
Ni
g
eria
n
M
e
tr
ol
og
i
c
a
l
A
ge
nc
y
(
N
i
Me
t)
.
F
i
gu
r
e
3
s
h
o
w
s
the
m
on
thl
y
av
erage
of
46
y
e
ars
da
t
a.
T
he
m
ax
i
m
u
m
s
ol
ar
r
ad
i
ati
on
i
s
r
ec
orde
d
i
n
Ma
r
c
h
wi
th
an
a
v
erag
e
of
25
.15
MJ
/m
2
/da
y
a
nd
A
ug
us
t
ha
s
the
m
i
ni
m
u
m
w
i
th
a
n
av
era
ge
of
19
.5
7M
J
/m
2
/da
y
.
T
he
m
on
ths
wi
th
t
he
l
o
wes
t
s
ol
ar
r
a
di
at
i
o
n
c
oi
nc
i
de
d
w
i
th
t
he
r
ai
n
y
s
ea
s
o
n
as
s
uc
h
the
i
nf
l
u
en
c
e
of
c
l
ou
d
c
ov
er
i
s
i
m
m
i
ne
nt.
Mo
r
eo
v
e
r
,
the
s
um
m
er
s
ea
s
on
s
ho
w
s
t
he
m
on
ths
wi
th
the
hi
gh
es
t
v
a
l
ue
s
of
s
ol
ar r
a
di
a
ti
o
n.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
no
v
e
l
mo
d
el
f
or s
ol
ar r
ad
i
ati
o
n p
r
e
di
c
t
i
on
(
I
brah
i
m
S
.
Ma
du
gu
)
3105
5.2
. Bo
x a
n
d
J
enkins
A
R
M
A
M
o
d
ell
ing
Y
ea
r
l
y
m
i
ni
m
um
av
erage
s
ol
ar
r
a
di
ati
on
i
s
c
on
s
i
de
r
ed
to
v
a
l
i
da
te
th
e
d
ev
el
o
pe
d
m
od
el
F
i
gu
r
e
4
s
h
o
w
s
a
ti
m
e
pl
ot
of
the
d
ata
.
A
dd
i
ng
a
tr
en
d
l
i
ne
tes
t
t
he
s
t
ati
on
ar
i
t
y
of
t
he
t
i
m
e
s
erie
s
f
ou
nd
the
s
l
op
e,
m
to
be
-
0.0
3
94
.
H
o
w
e
v
er,
th
e
f
i
r
s
t
di
f
f
erenc
e
of
the
da
ta
s
h
o
wed
a
s
l
op
e
of
m
=
0.0
00
4
th
at
i
s
al
m
os
t
z
ero
a
nd
m
a
k
es
the
ti
m
e
s
erie
s
s
tat
i
on
ar
y
.
T
he
A
uto
c
orr
el
ati
on
F
un
c
ti
o
n
(
A
CF
)
an
d
pa
r
t
i
a
l
au
toc
orr
e
l
at
i
on
f
un
c
ti
on
(
P
A
CF
)
p
l
ots
s
ho
wn
i
n
F
i
g
ure
s
5
(
a)
an
d
(
b)
r
es
pe
c
ti
v
el
y
s
ho
w
t
ha
t
s
ev
era
l
l
ag
s
(
k
)
are
w
i
t
hi
n
95
%
c
on
f
i
de
nc
e
i
n
terv
al
(
CI)
bo
u
nd
s
(
±
1
.
96
√
⁄
or
±
0.2
88
9,
where
N
=
46
)
,
he
nc
e
a
s
tat
i
on
ar
y
t
i
m
e
s
erie
s
.
T
he
A
CF
de
c
a
y
s
i
n
an
os
c
i
l
l
at
i
on
f
orm
af
ter
the
s
ec
on
d
l
ag
a
nd
the
P
A
CF
pl
ot
c
uts
of
f
j
us
t
af
ter
f
ew
l
ag
s
i
nd
i
c
ati
ng
A
RM
A
(
2,0
)
or hi
gh
er r
a
nk
.
Le
as
t
s
q
ua
r
e
pa
r
am
ete
r
es
ti
m
ati
on
m
eth
od
i
s
us
e
d
t
o
c
om
pu
te
s
ev
era
l
A
RM
A
m
od
e
l
s
;
i
nc
l
u
di
ng
A
R
MA
(
1,
0),
A
RM
A
(
1,1
)
,
A
R
MA
(
2
,0),
A
RM
A
(
2,1
)
,
A
RM
A
(
3,
0) a
nd
A
R
M
A
(
3,1
)
.
In
T
ab
l
e
1
the
A
I
C
an
d
m
ea
n
s
qu
ar
e
err
or
(
MS
E
)
of
al
l
th
e
m
o
de
l
s
are
pres
e
nte
d
wi
th
A
R
MA
(
3,
0)
ha
v
i
n
g
the
l
o
w
es
t
v
a
l
u
es
of
A
IC
a
nd
M
S
E
at
15
.2
00
6
an
d
-
0.0
1
94
3.
T
he
r
ef
ore,
A
RM
A
(
3,0
)
i
s
c
ho
s
e
n
as
th
e m
os
t p
ars
i
m
on
i
ou
s
m
od
el
.
T
he
A
RM
A
(
3,0
)
m
od
el
i
ns
ti
tut
es
th
at
t
he
y
e
arl
y
m
ea
n
s
ol
ar
r
ad
i
at
i
on
,
y
t
d
ep
e
n
ds
on
0.4
6
74
,
1
of
the
v
al
ue
a
y
e
ar
be
f
ore
(
−
1
)
s
ub
tr
ac
ted
b
y
0.0
4
66
,
2
of
the
v
al
ue
of
2
y
e
ars
be
f
ore
−
2
ad
d
ed
to
0.0
8
20
,
3
of
the
v
al
ue
3
y
ea
r
s
be
f
ore
p
l
us
a
r
an
do
m
v
ari
ab
l
e,
of
(
-
0.0
84
3).
T
he
m
ea
n,
μ
of
t
he
r
an
do
m
v
ari
ab
l
e
i
s
0.0
0
04
a
nd
a
s
ta
nd
ard
de
v
i
at
i
o
n,
σ
of
1.1
19
4.
T
he
ti
m
e
pl
ot,
A
CF
an
d
P
A
CF
of
the
r
es
i
d
ua
l
err
or
of
the
m
od
el
A
R
MA
(
3,
0)
di
s
p
l
a
y
e
d
i
n
F
i
gu
r
e
s
6
(
a)
a
nd
(
b)
ha
s
al
m
os
t
al
l
of
the
l
a
gs
of
the
c
orr
e
l
at
i
on
s
wi
t
hi
n
th
e
CI
bo
u
nd
s
.
T
he
ti
m
e
pl
ot
of
the
r
es
i
du
a
l
i
n
F
i
gu
r
e
7
i
s
a
be
h
av
i
n
g
l
i
k
e
a
w
hi
t
e
no
i
s
e
w
i
t
h
ap
pr
o
x
i
m
ate
l
y
z
er
o
m
ea
n (μ
=
0.0
0
6). T
hi
s
po
i
nt
to
th
e s
ui
t
ab
i
l
i
t
y
of
A
RM
A
(
3
,0) to t
he
d
ata
.
T
he
m
od
el
A
R
MA
(
3,
0)
i
s
us
ed
to
f
orec
as
t
the
s
o
l
ar
r
ad
i
at
i
o
n
da
t
a
an
d
the
r
e
s
ul
t
i
n
F
i
gu
r
e
8
s
h
o
w
s
a
go
o
d
ag
r
ee
m
en
t
be
t
w
e
en
th
e
ac
tua
l
da
ta
a
nd
th
e
f
orec
as
ted
d
ata
.
T
he
err
or
an
a
l
y
s
i
s
f
or
al
l
the
s
e
l
ec
ted
m
od
el
s
a
l
s
o
s
h
o
w
tha
t
A
R
MA
(
3,
0)
h
as
th
e
l
o
wes
t
v
a
l
ue
s
o
f
MA
P
E
,
RMS
E
a
nd
S
S
E
a
t 0
.
04
2
2,
0.0
4
00
2
an
d
0.
0
38
8 a
s
pre
s
en
ted
i
n T
ab
l
e 2
.
F
i
gu
r
e
3.
M
on
t
hl
y
a
v
era
ge
en
erg
y
(
19
71
-
2
01
6)
F
i
gu
r
e
4.
T
i
m
e
pl
ot
f
or
y
e
arl
y
m
i
n
i
m
u
m
s
ol
ar
r
ad
i
at
i
o
n (19
71
-
20
16
)
(
a)
(
b)
F
i
gu
r
e
5.
(
a)
A
uto
c
orr
el
at
i
o
n Func
ti
on
(
A
CF
)
of
s
ol
ar r
a
di
ati
on
(
1
97
1
-
2
01
6) t
i
m
e
s
erie
s
(
b) Pa
r
ti
al
A
ut
oc
orr
el
ati
on
F
un
c
ti
o
n (P
A
CF
)
of
s
ol
ar r
a
d
i
at
i
on
(
1
97
1
-
20
1
6) ti
m
e s
erie
s
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
31
0
0
-
31
0
9
3106
(
a)
(
b)
F
i
gu
r
e
6.
(
a)
A
uto
c
orr
el
at
i
o
n Func
ti
on
(
A
CF
)
p
l
ot
of
r
es
i
du
a
l
s
of
A
RM
A
(
3,
0)
(
b) Pa
r
ti
al
A
ut
oc
orr
el
ati
on
F
un
c
ti
o
n (P
A
CF
)
p
l
ot
of
r
es
i
du
a
l
s
of
A
RM
A
(
3,
0)
F
i
gu
r
e
7.
T
i
m
e
pl
ot
of
r
es
i
d
ua
l
s
of
A
RMA
(
3,0
)
F
i
gu
r
e
8.
M
ea
s
ure
d V
s
A
R
MA
(
3,
0) of
m
ea
n
y
e
ar
l
y
m
i
ni
m
u
m
s
ol
ar r
ad
i
at
i
on
(
1
97
1
-
20
1
6)
T
ab
l
e
1.
AI
C
an
d
M
S
E
V
a
l
u
es
of
A
RM
A
M
od
e
l
s
A
R
M
A
(
1
,
0
)
A
R
M
A
(
1
,
1
)
A
R
M
A
(
2
,
0
)
A
R
M
A
(
2
,
1
)
A
R
M
A
(
3
,
0
)
A
R
M
A
(
3
,
1
)
AIC
1
8
.
2
7
7
6
2
6
.
9
1
9
1
1
7
.
1
5
2
4
2
6
.
9
1
9
1
1
5
.
2
0
0
6
2
3
.
4
5
6
7
M
S
E
-
0
.
8
3
7
2
6
-
0.
80962
-
0.
81788
-
1.
9479
-
0.
01943
1.
8346
T
ab
l
e 2
.
R
MS
E
,
MA
P
E
, a
n
d
S
S
E
V
al
ue
s
of
A
R
MA
Mo
de
l
s
M
OD
E
L
R
M
S
E
M
A
P
E
S
S
E
A
R
M
A
(
1
,
0
)
0
.
0
1
8
2
1
.
8
2
0
1
7
7
.
5
6
0
9
A
R
M
A
(
1
,
1
)
0
.
0
1
7
6
1
.
7
6
0
0
7
7
.
5
7
6
2
A
R
M
A
(
2
,
0
)
0
.
0
1
7
8
1
.
7
7
8
0
7
7
.
5
7
1
5
A
R
M
A
(
2
,
1
)
0
.
0
4
2
3
4
.
2
3
4
7
7
7
.
5
5
5
9
A
R
M
A
(
3
,
0
)
0
.
0
0
0
4
0
.
0
4
2
2
0
.
0
3
8
8
5
A
R
M
A
(
3
,
1
)
0
.
0
3
9
9
3
.
9
8
8
2
6
9
.
9
8
9
6
5.3
.
A
RM
A
P
M
o
d
ell
ing
T
he
ne
w
A
R
MA
P
m
od
el
i
s
de
v
el
op
e
d
to
e
l
i
m
i
na
t
e
th
e
s
tat
i
on
ari
t
y
bo
tt
l
e
ne
c
k
s
u
c
h
as
ov
er
d
i
f
f
erenc
i
ng
,
s
tat
i
o
na
r
i
t
y
tes
t
a
nd
s
o
on
.
V
ari
ou
s
v
a
l
ue
s
of
V
n
(
w
h
ere
2
<
n
>
p
+
1
)
pa
r
am
ete
r
i
n
(
14
)
wer
e
s
e
l
ec
te
d
a
nd
t
he
A
RM
A
an
d
P
M
A
m
eth
o
do
l
og
y
i
s
f
ol
l
o
w
e
d
to
f
i
nd
t
he
be
s
t
m
od
el
.
O
nc
e
v
a
l
u
es
of
V
n
(
V
2
,
V
3
and
V
4
)
are
tab
ul
ate
d
the
n
i
t
c
an
be
us
ed
t
o
es
t
i
m
ate
pa
r
am
ete
r
s
o
f
the
A
RM
A
us
i
ng
d
i
f
f
erent
m
eth
od
s
s
uc
h
as
l
ea
s
t
s
qu
are
es
t
i
m
ati
on
,
m
ax
i
m
um
l
i
k
el
i
ho
od
,
Y
ul
e
-
W
al
k
er
es
ti
m
ate
etc
.
T
he
m
od
el
i
s
de
f
i
ne
d
as
A
RM
A
(
p,q
)
+
P
MA
(
n).
T
he
s
u
m
of
s
qu
are
err
or
(
S
S
E
)
of
v
ar
i
ou
s
P
MA
(
n)
i
nc
r
ea
s
es
as
n
i
s
greate
r
or
l
es
s
t
ha
n
p
or
q
as
s
ho
wn
i
n
F
i
gu
r
e
9,
w
h
ere
f
or
A
R
MA
(
3,0
)
,
P
M
A
(
2)
ha
s
S
S
E
of
9
3.9
5
18
tha
t
i
s
gre
ate
r
tha
n
c
orr
es
po
nd
i
ng
P
M
A
(
3)
wi
th
4.
17
X
10
-
23
.
Ho
w
e
v
er,
S
S
E
v
al
ue
of
P
MA
(
3)
i
s
l
es
s
th
an
tha
t
o
f
P
MA
(
4)
w
i
th
6.1
4X
10
-
21
.
B
as
ed
on
the
r
ul
e
of
pa
r
s
i
m
on
y
A
RM
A
(
3,
0)+
P
MA
(
3)
i
s
s
el
ec
ted
as
ad
eq
ua
t
e
w
i
th
a
be
tte
r
f
i
t
of
48
%
t
ha
n
A
R
MA
(
3,
0).
T
he
p
l
ot
of
f
orec
as
ted
a
ga
i
ns
t
th
e
ac
t
ua
l
d
at
a
i
s
s
h
o
w
n
i
n
F
i
gu
r
e
1
0
w
h
ere
the
c
orr
e
l
at
i
on
i
s
al
m
os
t
10
0%.
T
he
S
S
E
,
R
MS
E
an
d
M
A
P
E
f
or
the
m
od
el
are
1
.
8708
×
10
−
21
,
1
.
0444
×
10
−
10
and
6
.
6292
×
10
−
12
r
es
pe
c
ti
v
e
l
y
.
5.4
. Com
p
ar
i
son
bet
w
ee
n
A
RM
A
and
A
RM
A
P
Fo
r
ec
as
t
T
he
A
RM
A
P
m
od
el
i
m
pr
ov
es
t
he
A
RM
A
m
od
el
s
uc
h
tha
t
th
e
f
orec
as
t
i
s
be
tte
r
.
T
he
r
es
i
du
a
l
s
of
pred
i
c
ti
o
n
w
i
t
h
ea
c
h
m
od
el
ar
e
us
e
d
f
or
v
ario
us
err
or
an
a
l
y
s
e
s
to
de
term
i
ne
the
be
s
t
m
od
el
tha
t
f
i
ts
the
da
t
a.
T
he
s
e
err
or
an
a
l
y
s
e
s
m
a
y
i
nc
l
u
de
s
um
of
s
qu
a
r
e
err
or
(
S
S
E
)
,
s
u
m
of
err
or
(
S
E
)
,
m
ea
n
ab
s
ol
ute
p
erc
en
ta
ge
err
or
(
M
A
P
E
)
,
r
o
ot
m
ea
n
s
qu
are
er
r
or
an
d
T
he
i
l
’
s
U
-
S
tat
i
s
ti
c
s
.
A
s
pro
v
en
i
nt
er
-
al
i
a
A
R
MA
(
3
,0)
m
od
el
i
s
f
ou
nd
to
be
th
e
be
s
t
am
on
g
th
e
tes
te
d
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
no
v
e
l
mo
d
el
f
or s
ol
ar r
ad
i
ati
o
n p
r
e
di
c
t
i
on
(
I
brah
i
m
S
.
Ma
du
gu
)
3107
m
od
el
s
.
A
l
s
o,
th
e
i
ntrod
u
c
ti
on
of
A
RM
A
P
s
ho
w
s
a
great
i
m
prov
em
e
nt
i
n
th
e
ti
m
e
s
erie
s
f
orec
as
ti
ng
,
whereb
y
t
he
r
e
i
s
trem
en
do
us
r
ed
uc
t
i
on
i
n
err
or ana
l
y
s
i
s
.
Fi
gu
r
e
9.
S
um
of
S
qu
are
E
r
r
or of
A
RM
A
(
3,0
)
+
P
MA
(
n)
F
i
gu
r
e
10
.
A
R
MA
(
3,
0)+
P
M
A
(
3) F
orec
as
ti
ng
5.5
.
A
n
al
y
s
is
o
f
S
u
m o
f
S
q
u
ar
e
E
r
r
o
r
f
o
r
A
RM
A
an
d
A
RM
A
P
T
he
s
u
m
s
o
f
s
qu
are
err
ors
of
the
two
m
eth
od
s
are
c
om
pa
r
ed
as
s
ho
wn
i
n
F
i
g
u
r
e
11
.
I
t
c
an
be
d
ed
uc
e
d
t
ha
t
P
MA
(
3)
f
or
A
RM
A
(
3,0
)
an
d
A
R
MA
(
4
,0)
h
av
e
t
he
l
ea
s
t
v
a
l
u
es
w
i
th
1.87
x
10
-
21
a
nd
2.6
8
x
10
-
22
r
es
pe
c
ti
v
e
l
y
wh
i
l
e
P
MA
(
2)
+
A
RM
A
(
2,0
)
ha
s
th
e h
i
g
he
s
t
v
a
l
ue
(
25
5
.75
)
.
Cons
i
d
erin
g
th
e
pr
i
nc
i
pl
e
of
pa
r
s
i
m
on
y
A
R
MA
(
3,0
)
wi
l
l
b
e
c
ho
s
e
n
a
nd
c
om
pa
r
ed
wi
th
A
RM
A
(
3,0
)
+
P
MA
(
3). T
he
S
S
E
of
th
es
e t
wo m
od
el
s
are
55
.
13
an
d
1.8
7
x
10
-
21
f
or A
RMA
(
3,
0) a
nd
A
RM
A
(
3,0
)
+
P
MA
(
3)
r
es
pe
c
ti
v
el
y
r
ep
r
es
en
t
i
ng
a red
uc
ti
on
of
err
or b
y
6.
60
x
10
17
%.
5.6
.
A
n
al
y
s
is
o
f
T
h
eil
’s
U
-
S
t
atist
ic
f
o
r
A
RM
A
and
A
RM
A
P
T
he
T
he
i
l
’
s
U
-
s
tat
i
s
t
i
c
s
d
e
s
c
r
i
be
d
i
n
e
qu
at
i
o
n
18
i
s
an
oth
er
a
na
l
y
s
i
s
th
at
de
s
c
r
i
be
s
the
pe
r
f
orm
an
c
e
of
f
orec
a
s
ti
ng
m
od
el
,
us
ua
l
l
y
th
e
m
od
e
l
w
i
t
h
the
l
o
w
es
t
v
al
ue
i
s
c
on
s
i
de
r
ed
the
b
es
t
m
od
el
.
In
F
i
gu
r
e
12
A
RM
A
(
3,0
)
h
as
a
v
a
l
ue
0.0
0
61
whi
c
h
i
s
hi
g
he
r
tha
n
A
RM
A
(
3,0
)
+
P
MA
(
3)
ha
v
i
n
g
3.6
9X
1
0
-
14
.
H
o
w
e
v
er,
i
t
c
an
be
s
ee
n
t
ha
t
A
RM
A
(
4
,0)
ha
s
a
v
er
y
s
l
i
gh
t l
o
w
er
v
a
l
ue
bu
t
i
s
qu
i
t
e i
ns
i
gn
i
f
i
c
an
t a
n
d
as
s
uc
h i
t i
s
no
t c
on
s
i
de
r
ed
.
F
i
gu
r
e
11
.
S
um
s
qu
are err
o
r
of
A
RMA
an
d
A
RM
A
P
m
od
el
s
F
i
gu
r
e
12
. T
he
i
l
’
s
U
-
S
ta
ti
s
ti
c
f
or ARM
A
an
d
A
RM
A
P
m
od
el
s
5.7
.
A
n
al
y
s
is
o
f
Ro
o
t
M
ea
n
S
q
u
ar
e E
r
r
o
r
(
RM
S
E
)
f
o
r
A
RM
A
and
A
RM
A
P
T
he
m
od
el
w
i
t
h
l
o
wes
t
r
oo
t
m
ea
n
s
qu
are
err
or
de
s
c
r
i
b
ed
i
n
eq
u
ati
on
3.
37
i
s
c
on
s
i
de
r
e
d
the
b
es
t
m
od
el
.
In
F
i
g
ure
13
th
e
v
al
ue
1
.04
44
X
10
-
10
A
RM
A
(
3,0
)
+
P
MA
(
3)
f
or
i
s
the
l
o
w
es
t
a
nd
he
nc
e
th
e
be
s
t
m
od
el
.
F
urt
he
r
m
ore,
c
o
m
pa
r
i
ng
the
R
MS
E
v
a
l
u
e
of
17
.21
64
f
or
A
RM
A
(
3,0
)
a
nd
A
RM
A
P
c
ou
nt
erpar
t
wi
l
l
i
nd
i
c
ate
a d
i
f
f
erenc
e o
f
a
v
a
l
ue
m
ore tha
n 1
b
i
l
l
i
on
.
Evaluation Warning : The document was created with Spire.PDF for Python.
◼
IS
S
N: 16
93
-
6
93
0
T
E
L
KO
M
NIK
A
V
ol
.
17
,
No
.
6,
D
ec
em
be
r
20
19
:
31
0
0
-
31
0
9
3108
5.8
.
A
n
al
y
s
is
o
f
M
ea
n
A
b
solu
t
e P
er
c
ent
age
E
r
r
o
r
(
M
A
P
E
)
f
o
r
A
RM
A
and
A
R
M
A
P
T
hi
s
i
s
an
oth
er
pa
r
am
ete
r
us
ed
to
c
ho
os
e
t
he
be
s
t
m
od
el
tha
t
f
i
t
a
da
t
a.
F
i
g
ure
14
s
ho
w
s
the
a
na
l
y
s
i
s
of
thi
s
pa
r
am
ete
r
an
d
i
t
c
an
b
e
s
ee
n
th
at
w
h
i
l
e
A
R
MA
m
o
de
l
s
tarts
wi
th
a
v
er
y
hi
gh
v
al
ue
f
or
A
R
MA
(
1,
0)
i
t
de
c
r
ea
s
es
up
t
o
A
RM
A
(
4,
0).
Ho
w
e
v
er,
t
he
pa
t
tern
f
or
A
RM
A
P
m
od
el
s
s
tarts
wi
th
l
o
w
er
v
a
l
u
es
, i
nc
r
e
as
es
an
d d
ec
r
ea
s
e
d t
o
th
e
l
o
wes
t
v
al
u
e.
F
i
gu
r
e
13
.
Root
m
a
en
s
qu
a
r
e e
r
r
or of
A
RM
A
an
d
A
RM
A
P
m
od
el
s
F
i
gu
r
e
14
.
Me
an
a
bs
ol
ute
p
erc
en
tag
e e
r
r
or of
A
RM
A
a
nd
A
RM
A
P
m
od
el
s
6.
Co
n
clus
ion
In
th
i
s
pa
pe
r
t
i
m
e
s
erie
s
B
ox
an
d
en
k
i
ns
m
eth
od
o
l
og
y
i
s
us
ed
to
f
i
n
d
a
be
s
t
m
od
el
f
or
f
orec
as
ti
ng
m
ea
n
y
ea
r
l
y
s
o
l
ar
r
ad
i
a
ti
o
n
da
ta
of
46
y
ea
r
s
,
be
t
w
ee
n
19
71
a
nd
2
01
6
.
Res
ul
ts
s
ho
w
tha
t
A
RM
A
(
3,
0)
m
od
el
i
s
the
m
os
t
pa
r
s
i
m
on
i
ou
s
a
nd
f
i
ts
the
da
t
a
b
ett
er
t
ha
n
oth
er
c
ho
s
en
m
od
el
s
w
i
t
h
th
e
l
o
w
es
t
RM
S
E
v
a
l
ue
of
0.0
00
4
an
d
S
S
E
v
a
l
ue
of
0.0
38
85
.
A
ne
wl
y
de
v
e
l
op
ed
proc
ed
ure
us
i
ng
a
h
y
br
i
d
m
eth
od
i
s
f
ou
nd
to
i
m
pr
ov
e
t
he
f
orec
as
t
an
d
r
ed
uc
ed
the
err
or
be
t
w
e
en
the
ac
t
ua
l
a
nd
th
e
f
orec
as
ted
da
t
a.
A
R
MA
P
pro
v
ed
to
b
e
a
b
ett
er
f
orec
as
ti
ng
m
od
el
where
i
ts
c
orr
es
p
on
di
n
g
v
al
ue
s
of
RMS
E
,
MA
P
E
an
d S
S
E
are m
uc
h l
o
w
er.
Ref
er
en
ce
s
[1
]
Das
UK,
T
e
y
KS,
Se
y
e
d
m
a
h
m
o
u
d
i
a
n
M
,
M
e
k
h
i
l
e
f
S,
Id
ri
s
M
Y
,
Va
n
Dev
e
n
te
r
W
,
Hora
n
B,
Sto
j
c
e
v
s
k
i
A
.
Fo
re
c
a
s
ti
n
g
o
f
p
h
o
t
o
v
o
l
ta
i
c
p
o
w
e
r
g
e
n
e
r
a
ti
o
n
a
n
d
m
o
d
e
l
o
p
ti
m
i
z
a
ti
o
n
:
A
re
v
i
e
w
.
Ren
e
wab
l
e
a
n
d
Su
s
ta
i
n
a
b
l
e
En
e
rg
y
Re
v
i
e
ws
.
2018
;
81
:
912
-
928
.
[2
]
Cou
n
c
i
l
WE
.
W
o
rl
d
e
n
e
rg
y
s
c
e
n
a
ri
o
s
c
o
m
p
o
s
i
n
g
e
n
e
rg
y
f
u
tu
r
e
s
t
o
2
0
5
0
.
PSI,
L
o
n
d
o
n
.
2
0
1
3
.
[3
]
Ak
o
re
d
e
MF
,
Ib
ra
h
i
m
O
,
A
m
u
d
a
SA
,
O
tu
o
z
e
AO
,
O
l
u
f
e
a
g
b
a
BJ
.
C
u
rre
n
t
ta
tu
a
n
d
o
u
tl
o
o
k
o
f
re
n
e
w
a
b
l
e
e
n
e
rg
y
d
e
v
e
l
o
p
m
e
n
t
i
n
Nig
e
r
i
a
.
Nig
e
ri
a
n
J
o
u
r
n
a
l
o
f
Te
c
h
n
o
l
o
g
y
(NI
J
O
TECH)
.
2017
;
36
:
196
-
2
1
2
.
[4
]
Ab
d
u
l
k
a
ri
m
A
,
Ab
d
e
l
k
a
d
e
r
S,
M
o
rro
w
DJ
.
Sta
t
i
s
t
i
c
a
l
a
n
a
l
y
s
e
s
o
f
wi
n
d
a
n
d
s
o
l
a
r
e
n
e
rg
y
r
e
s
o
u
rc
e
s
fo
r
th
e
d
e
v
e
l
o
p
m
e
n
t
o
f
h
y
b
r
i
d
m
i
c
ro
g
ri
d
.
2
nd
In
te
r
n
a
ti
o
n
a
l
Co
n
g
re
s
s
o
n
En
e
rg
y
Eff
i
c
i
e
n
c
y
a
n
d
En
e
rg
y
Rel
a
te
d
M
a
te
ri
a
l
s
(ENEFM
2
0
1
4
) Sp
ri
n
g
e
r Pro
c
e
e
d
i
n
g
s
i
n
En
e
rg
y
.
Sw
i
tz
e
rl
a
n
d
.
2
0
1
5
:
9
-
14
.
[5
]
M
e
k
o
n
ts
o
C
,
A
b
d
u
l
k
a
r
i
m
A
,
M
a
d
u
g
u
IS
,
I
b
ra
h
i
m
O
,
A
d
e
d
i
ra
n
YA
.
Rev
i
e
w
o
f
O
p
ti
m
i
z
a
ti
o
n
T
e
c
h
n
i
q
u
e
s
fo
r
Si
z
i
n
g
Re
n
e
w
a
b
l
e
E
n
e
rg
y
Sy
s
te
m
s
.
Com
p
u
te
r
En
g
i
n
e
e
r
i
n
g
a
n
d
Ap
p
l
i
c
a
ti
o
n
s
.
2
0
1
9
;
8
(
1
)
:
13
-
3
0
.
[6
]
An
o
l
i
e
fo
E
.
T
h
e
ro
l
e
o
f
d
u
s
t
i
n
t
h
e
f
a
i
l
u
re
m
e
c
h
a
n
i
s
m
o
f
s
o
l
a
r
s
tre
e
t
l
i
g
h
t
i
n
Ni
g
e
ri
a
.
J
o
u
r
n
a
l
o
f
Ren
e
wab
l
e
a
n
d
Al
t
e
rn
a
t
i
v
e
En
e
rg
y
T
e
c
h
n
o
l
o
g
i
e
s
.
2
0
1
6
;
2
:
86
-
93.
[7
]
Chi
e
m
e
k
a
OO
,
O
n
u
r
T
,
Dere
k
KB
.
S
o
l
a
r
e
n
e
r
g
y
p
o
t
e
n
ti
a
l
s
i
n
s
tra
t
e
g
i
c
a
l
l
y
l
o
c
a
t
e
d
c
i
ti
e
s
i
n
Nig
e
ri
a
:
Rev
i
e
w
,
re
s
o
u
r
c
e
a
s
s
e
s
s
m
e
n
t
a
n
d
PV
s
y
s
te
m
d
e
s
i
g
n
.
R
e
n
e
wab
l
e
a
n
d
Su
s
ta
i
n
a
b
l
e
En
e
rg
y
Re
v
i
e
ws
.
2016
;
55
:
550
-
5
6
6
.
[8
]
M
o
h
a
m
m
e
d
S,
Pe
ti
n
ri
n
JO
.
Ren
e
w
a
b
l
e
e
n
e
rg
y
p
o
te
n
t
i
a
l
s
i
n
Ni
g
e
ri
a
:
m
e
e
t
i
n
g
ru
ra
l
e
n
e
rg
y
n
e
e
d
s
.
Ren
e
wab
l
e
a
n
d
Su
s
ta
i
n
a
b
l
e
E
n
e
rg
y
Re
v
i
e
ws
.
2
0
1
4
:
72
-
84.
[9
]
Vi
n
c
e
n
t
EN,
Y
u
s
u
f
SD
.
In
te
g
r
a
ti
n
g
R
e
n
e
w
a
b
l
e
E
n
e
rg
y
a
n
d
Sm
a
rt
G
ri
d
T
e
c
h
n
o
l
o
g
y
i
n
to
th
e
Nig
e
ri
a
n
El
e
c
tr
i
c
i
ty
Grid
Sy
s
te
m
.
Sm
a
rt
g
ri
d
a
n
d
Re
n
e
wab
l
e
En
e
rg
y
.
2
0
1
4
;
5
(0
9
)
:
2
2
0
-
2
3
8
.
[1
0
]
M
o
h
a
m
m
e
d
Y
,
M
u
s
ta
fa
M
,
Ba
s
h
i
r
N,
M
o
k
h
ta
ra
A
.
Ren
e
w
a
b
l
e
e
n
e
r
g
y
re
s
o
u
rc
e
s
fo
r
d
i
s
tri
b
u
te
d
p
o
w
e
r
g
e
n
e
ra
ti
o
n
i
n
Ni
g
e
ri
a
:
A
re
v
i
e
w
o
f
th
e
p
o
te
n
t
i
a
l
.
Ren
e
wa
b
l
e
a
n
d
Su
s
ta
i
n
a
b
l
e
En
e
r
g
y
Re
v
i
e
ws
j
o
u
r
n
a
l
.
2013
:
257
-
268.
[1
1
]
Ad
e
o
ti
O
,
O
y
e
w
o
l
e
BA,
Ad
e
g
b
o
y
e
g
a
T
D
.
So
l
a
r
p
h
o
to
v
o
l
ta
i
c
-
b
a
s
e
d
h
o
m
e
e
l
e
c
t
ri
fi
c
a
t
i
o
n
s
y
s
te
m
f
o
r
ru
ra
l
d
e
v
e
l
o
p
m
e
n
t
i
n
Ni
g
e
r
i
a
:
d
o
m
e
s
ti
c
l
o
a
d
a
s
s
e
s
s
m
e
n
t
.
Re
n
e
wab
l
e
E
n
e
rg
y
.
2
0
0
1
;
2
4
(1
)
:
1
5
5
-
161
.
Evaluation Warning : The document was created with Spire.PDF for Python.
T
E
L
KO
M
NIK
A
IS
S
N: 1
69
3
-
6
93
0
◼
A
no
v
e
l
mo
d
el
f
or s
ol
ar r
ad
i
ati
o
n p
r
e
di
c
t
i
on
(
I
brah
i
m
S
.
Ma
du
gu
)
3109
[1
2
]
Ab
d
u
l
k
a
ri
m
A
,
Ab
d
e
l
k
a
d
e
r
S,
M
o
rro
w
D
.
M
e
th
o
d
fo
r
o
p
t
i
m
u
m
d
e
s
i
g
n
o
f
s
ta
n
d
a
l
o
n
e
h
y
b
ri
d
re
n
e
w
a
b
l
e
e
n
e
rg
y
m
i
c
ro
g
ri
d
s
.
J
o
u
r
n
a
l
o
f
Fu
n
d
a
m
e
n
ta
l
a
n
d
A
p
p
l
i
e
d
S
c
i
e
n
c
e
s
.
2
0
1
7
;
9
(
2
)
:
1047
-
1
1
0
1
.
[1
3
]
Sc
h
n
i
tz
e
r
D
,
L
o
u
n
s
b
u
ry
D
,
Carv
a
l
l
o
J
,
De
s
h
m
u
k
h
R
,
A
p
t
J
,
Ka
m
m
e
n
DM
.
M
i
c
ro
g
ri
d
s
f
o
r
ru
r
a
l
e
l
e
c
tri
f
c
a
ti
o
n
:
a
c
r
i
ti
c
a
l
r
e
v
i
e
w
o
f
b
e
s
t
p
ra
c
ti
c
e
s
b
a
s
e
d
o
n
s
e
v
e
n
c
a
s
e
s
tu
d
i
e
s
.
Uni
t
e
d
Nat
i
o
n
s
Fo
u
n
d
a
ti
o
n
.
Cal
i
fo
r
n
i
a
,
B
e
rk
e
l
e
y
.
2014.
[1
4
]
Bu
g
a
j
e
IM
.
Rem
o
te
a
re
a
p
o
wer
s
u
p
p
l
y
i
n
Nig
e
ri
a
:
t
h
e
p
ro
s
p
e
c
ts
o
f
s
o
l
a
r
e
n
e
rg
y
.
Ren
e
wa
b
l
e
En
e
rg
y
.
1999
;
1
8
(4
)
:
491
-
500.
[1
5
]
Ab
d
u
l
k
a
ri
m
A
,
Ab
d
e
l
k
a
d
e
r
SM
,
M
o
rro
w
D
,
Am
u
d
a
S
,
M
a
d
u
g
u
S
,
Fa
l
a
d
e
A
,
Sa
m
i
n
u
S,
Ad
e
d
i
ra
n
A
.
Eff
e
c
t
s
o
f
PV
te
c
h
n
o
l
o
g
y
o
n
th
e
o
p
ti
m
a
l
d
e
s
i
g
n
o
f
s
ta
n
d
a
l
o
n
e
re
n
e
w
a
b
l
e
e
n
e
r
g
y
m
i
c
ro
g
r
i
d
.
J
o
u
r
n
a
l
o
f
El
e
c
tr
i
c
a
l
e
n
g
i
n
e
e
ri
n
g
En
g
i
n
e
e
ri
n
g
.
2018
;
17
(
1
)
:
1
-
8
.
[1
6
]
Has
s
a
n
J
.
ARIM
A
a
n
d
re
g
re
s
s
i
o
n
m
o
d
e
l
s
fo
r
p
re
d
i
c
ti
o
n
o
f
d
a
i
l
y
a
n
d
m
o
n
th
l
y
c
l
e
a
rn
e
s
s
i
n
d
e
x
.
Ren
e
wab
l
e
En
e
r
g
y
.
2
0
1
4
;
68
(
1)
:
4
2
1
-
7
.
[1
7
]
Kh
a
re
V,
Ne
m
a
S,
Ba
re
d
a
r
P
.
So
l
a
r
–
w
i
n
d
h
y
b
ri
d
re
n
e
w
a
b
l
e
e
n
e
rg
y
s
y
s
te
m
:
A
r
e
v
i
e
w
.
Ren
e
wab
l
e
and
Su
s
ta
i
n
a
b
l
e
En
e
rg
y
Re
v
i
e
ws
.
2
0
1
6
;
58
:
23
-
33.
[1
8
]
Hua
n
g
R,
Hu
a
n
g
T
,
G
a
d
h
R,
L
i
N
.
So
l
a
r
g
e
n
e
r
a
ti
o
n
p
re
d
i
c
ti
o
n
u
s
i
n
g
th
e
ARM
A
m
o
d
e
l
i
n
a
l
a
b
o
ra
to
ry
-
l
e
v
e
l
m
i
c
r
o
g
ri
d
.
IE
EE
T
h
i
rd
In
te
rn
a
t
i
o
n
a
l
Con
f
e
re
n
c
e
o
n
Sm
a
r
t
G
ri
d
Com
m
u
n
i
c
a
ti
o
n
s
.
2012
:
5
2
8
-
5
3
3
.
[1
9
]
W
a
n
Ah
m
a
d
W
K
A
,
Ah
m
a
d
S
.
Ari
m
a
m
o
d
e
l
a
n
d
e
x
p
o
n
e
n
t
i
a
l
s
m
o
o
th
i
n
g
m
e
th
o
d
:
a
c
o
m
p
a
ri
s
o
n
.
AI
P
Con
fe
re
n
c
e
Pr
o
c
e
e
d
i
n
g
s
.
2
0
1
3
;
1
5
2
2
(
1
):
1
3
1
2
-
1321
.
[2
0
]
Fe
rra
ri
S,
L
a
z
z
a
ro
n
i
M
,
Pi
u
ri
V,
Cri
s
ta
l
d
i
L
,
Fa
i
fe
r
M
.
Sta
ti
s
ti
c
a
l
m
o
d
e
l
s
a
p
p
ro
a
c
h
fo
r
s
o
l
a
r
ra
d
i
a
t
i
o
n
p
re
d
i
c
ti
o
n
.
IEEE
In
t
e
rn
a
t
i
o
n
a
l
In
s
tru
m
e
n
ta
ti
o
n
a
n
d
M
e
a
s
u
r
e
m
e
n
t
T
e
c
h
n
o
l
o
g
y
Con
f
e
re
n
c
e
(I2
M
T
C)
.
2013
:
1
7
3
4
-
1739
.
[2
1
]
W
u
J
,
Ch
a
n
CK
.
T
h
e
p
re
d
i
c
t
i
o
n
o
f
m
o
n
th
l
y
a
v
e
ra
g
e
s
o
l
a
r
r
a
d
i
a
ti
o
n
wit
h
TDNN
a
n
d
ARIM
A
.
2
0
1
2
1
1
th
In
te
rn
a
ti
o
n
a
l
Co
n
fe
re
n
c
e
o
n
M
a
c
h
i
n
e
L
e
a
rn
i
n
g
a
n
d
A
p
p
l
i
c
a
ti
o
n
s
.
2
0
1
2
;
2
:
4
6
9
-
474
.
[2
2
]
Sh
u
m
w
a
y
R,
Sto
ff
e
r
D. T
i
m
e
S
e
ri
e
s
An
a
l
y
s
i
s
.
L
o
n
d
o
n
:
Sp
ri
n
g
e
r
.
2
0
1
1
.
[2
3
]
M
c
G
e
e
R,
Y
a
ff
e
e
M.
In
tro
d
u
c
ti
o
n
to
ti
m
e
s
e
ri
e
s
a
n
a
l
y
s
i
s
a
n
d
fo
r
e
c
a
s
ti
n
g
.
Bro
o
k
l
y
n
,
New
Y
o
rk
:
Ac
a
d
e
m
i
c
Pre
s
s
,
In
c
.
1
9
9
9
.
[2
4
]
O
tu
ra
n
c
G
,
Hep
b
a
s
l
i
A,
G
e
n
c
A
.
Sta
t
i
s
t
i
c
a
l
a
n
a
l
y
s
i
s
o
f
s
o
l
a
r
ra
d
i
a
ti
o
n
d
a
ta
.
E
n
e
rg
y
So
u
r
c
e
s
.
2
0
1
0
;
25
(
11
)
:
1
0
8
9
-
1
0
9
7
.
[2
5
]
Pe
l
g
ri
n
F
.
L
e
c
t
u
re
5
:
Bo
x
-
J
e
n
k
i
n
s
m
e
t
h
o
d
o
l
o
g
y
.
Ni
c
e
.
2
0
1
1
.
Evaluation Warning : The document was created with Spire.PDF for Python.