ARMASIM Function

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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 moving-average 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 moving-average (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 Y₀,Y₁, ... ,Y_p+q-1 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

$Y_t = -\sum_{i=1}^p \phi_i Y_{t-i} + \epsilon_t + \sum_{i=1}^q \theta_i \epsilon_{t-i} t = p+q, p+q+1, ... , n-1 .$

The random number generator RANNOR is used to generate the noise component of the model. Note that the statement

armasim(1,1,0,1,n,seed);

returns n standard normal pseudo-random deviates.

For example, to generate a time series of length 10 from the model

y_t = 0.5y_t-1 + e_t + 0.8e_t-1

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

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