ARMASIM Function
simulates a univariate ARMA series
 ARMASIM( phi, theta, mu, sigma, n,
<seed>)
The inputs to the ARMASIM function are As follows:
 phi
 is a 1 ×(p+1) matrix containing
the autoregressive parameters.
The first element is assumed to have the value 1.
 theta
 is a 1 ×(q+1) matrix containing
the movingaverage parameters.
The first element is assumed to have the value 1.
 mu
 is a scalar containing the overall mean of the series.
 sigma
 is a scalar containing the standard
deviation of the innovation series.
 n
 is a scalar containing n, the length of the series.
The value of n must be greater than 0.
 seed
 is a scalar containing the random number seed.
If it is not supplied, the system clock is used to generate the seed.
If it is negative, then the absolute value is used as the starting
seed; otherwise, subsequent calls ignore the value of
seed and use the last seed generated internally.
The ARMASIM function generates a series of length n from
a given autoregressive movingaverage (ARMA) time series
model and returns the series in an n ×1 matrix.
The notational conventions for the ARMASIM function
are the same as those used by the ARMACOV subroutine.
See the description of the ARMACOV call for the model employed.
The ARMASIM function uses an exact simulation
algorithm as described in Woodfield (1988).
A sequence Y_{0},Y_{1}, ... ,Y_{p+q1} of starting
values is produced using an expanded covariance
matrix, and then the remaining values are generated
using the recursion form of the model, namely
The random number generator RANNOR is used
to generate the noise component of the model.
Note that the statement
returns n standard normal pseudorandom deviates.
For example, to generate a time series of length 10 from the model

y_{t} = 0.5y_{t1} + e_{t} + 0.8e_{t1}
use the following code to produce the result shown:
proc iml;
phi={1 0.5};
theta={1 0.8};
y=armasim(phi, theta, 0, 1, 10, 1234321);
print y;
Y
2.3253578
0.975835
0.376358
0.878433
2.515351
3.083021
1.996886
1.839975
0.214027
1.4786717
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.