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STAT 510 - Applied Time Series Analysis
•
ANGEL
•
Department of Statistics
•
Eberly College of Science
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Section 2: Time Domain Models
Forecasting Using the ARMA Model
Submitted by gfj100 on Sun, 03/28/2010 - 15:33
Let's talk about forecasting an
ARMA
. We assume that we've started with an
ARMA
model (which is of
course causal and invertible) and that we've estimated the parameters and they are EXACTLY right (not
realistic -- but let's go with it right now.) The model is:
We will assume for the moment that we know the coefficients of the model, the φ's and the θ's.
Now, because it is causal and invertible, then if we know the φ's and the θ's, we also know the π's and the
ψ's:
(the causal representation)
(the invertible representation)
Recall that the ψ's are:
and the π's are:
. Assume we know how to calculate
these.
In practice, what we will have is data that goes from
x
1
, .
..
x
n
and what we want to do is to predict in
future observations
x
n+
1
,
x
n+
2
...
x
n+m
.

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** preview**
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Let's define the tilde over
x
to mean:
This is the conditional expectation: given my data up to

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Node24 Forecasting Using the ARMA Model STAT 510 - Applied Time Series Analysis

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