STA457H1 Chapter Notes - Chapter 6: Autoregressive Integrated Moving Average

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8 Apr 2014
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Chapter 6 Non-stationary (ARIMA)
Time Series Models
6.1ARIMA models for non-stationary TS
Definition
If d is a non-negative integer, then
{
Xt
}
is an ARIMA(p,d,q) model if
Yt=
(
1B
)
dXt
is a causal
ARMA(p,q) process
In mathematical terms
Φ
(
B
) (
1B
)
dXt=Θ
(
B
)
Zt
ZtWN
(
0,σ2
)
Φ
(
B
)
has roots all outside of the unit circle
Properties
- ACF of ARIMA(p,d,q) is very slowly decaying
Suppose we have ARIMA(p,d,q) model
If we fit an AR(1) model to it, then the fitted AR coefficient will be close to 1
Note there are no ACF or PACF for ARIMA(p,d,q) for d>=1
However, sample ACF and PACF are still well defined
6.2 – Identification Techniques
(a) Preliminary transformation
- Trend removal (moving window, harmonic regression)
- Differentiation (ARIMA(
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