STA4005B
Time Series (2007-2008)
Tutorial 6 (26/2, 27/2)
(Time & Venue: T9, BMS LT; W5, MMW 704)
Definition:
A series
{
is said to follow an integrated autoregressive moving average model if the
difference
is a stationary ARMA process. If W
}
t
Z
th
d
t
d
t
Z
W
∇
=
t
is ARMA(p, q), we say that
{
}
t
Z
is ARIMA(p, d, q).
In general, the ARIMA(p, d, q) model can be expressed as
t
t
d
a
B
Z
B
B
)
(
)
(
)
1
(
θ
φ
=
−
where the stationary AR operator
and the invertible MA operator
share no common factors. This is useful form for identifying models.
p
p
B
B
B
B
φ
φ
φ
φ
−
−
−
−
=
L
2
2
1
1
)
(
q
q
B
B
B
B
θ
θ
θ
θ
−
−
−
−
=
L
2
2
1
1
)
(
Example 1
Given a process
, identify the model as a specific ARIMA model.
t
t
t
t
a
Z
Z
Z
+
−
=
−
−
2
1
25
.
0
25
.
1
1

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