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Auto-Regressive Simulation (Second-Order)

​
a
1
a
2
randomize
This Demonstration shows realizations of a second-order auto-regressive (AR) process
y
, using the random variable
r
drawn from a normal density with mean zero and variance unity. It is governed by the equation:
y
i
=
a
1
y
i-1
+
a
2
y
i-2
+
r
i
(
i=3,…,N
, where
N
is the length of the series).
The constants
a
1
and
a
2
are the auto-regressive constants. If
a
1
+
a
2
<1,
a
2
-
a
1
<1,and-1<
a
2
<1
, the series is stationary. A series of length 400 is created in every case.
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