H9
{}
t
X
is called an
autoregressive integrated moving average
(ARIMA) process
of order
(,,)
pdq
,
denoted as
~
A
R
I
M
A
(
,
,
)
t
X
, where
is an integer,
1
d
≥
if its
d
order difference
is a
casual
AR
(1
)
d
tt
YB
=−
X
MA( , )
p q
process,
i.e.,
2
()
() ,{ }
~WN
(
0
, )
t
BY
B Z
Z
φ
θσ
=
It is easy to see that an
ARIMA( , , )
model is a special
nonstationary
ARMA(
, )
p dq
+
model,
*( )
( )
B
XB
Z
θ
=
,
where
( )(1
)
d
B
BB
φφ
is a polynomial of order
p
d
+
.
Example 1
model
ARIMA(1,1,1)
(1 .5 )(1
)
(1 .3 )
B
BX
BZ
−−=
+
.
Example 2
Differencing an
ARMA( , )
p q
results in a noninvertible process.
Forecasts
for an
ARIMA( , , )
model,
*
11
pd
q
t
i ti
t
ii
X
XZ
Z
φθ
+
−
−
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This note was uploaded on 09/23/2009 for the course MATH 200 taught by Professor Gur during the Spring '09 term at Accreditation Commission for Acupuncture and Oriental Medicine.
 Spring '09
 gUR

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