VARMASIM Call
generates a VARMA(p,q) series
- CALL VARMASIM( series, phi, theta, mu, sigma, n
<, p, q, initial, seed>);
The inputs to the VARMASIM subroutine are as follows:
- phi
- specifies to a kp ×k matrix
containing the vector autoregressive coefficient matrices.
- theta
- specifies to a kq ×k matrix
containing the vector moving-average coefficient matrices.
You must specify either phi or theta.
- mu
- specifies a k ×1 (or 1 ×k) mean vector of the series.
By default, mu is a zero vector.
- sigma
- specifies a k ×k covariance matrix of the innovation series.
By default, sigma is an identity matrix with dimension k.
- n
- specifies the length of the series. By default, n=100.
- p
- specifies the order of VAR.
See the VARMACOV subroutine.
- q
- specifies the order of VMA.
See the VARMACOV subroutine.
- initial
- specifies the initial values of random variables.
If initial=a0, y-p+1, ... ,y0 and
take all the same value as
initial=a0.
If initial option is not specified,
the initial values are estimated using VARMACOV
for stationary vector time series, while the initial values assume as zero
values for nonstationary vector time series.
- seed
- specifies the random number seed.
See the VNORMAL subroutine.
The VARMASIM subroutine returns the following value:
- series
- refers an n×k matrices the generated VARMA(p,q) series.
When either initial option is specified or
the zero initial values are used, the returns do not print these initial
values.
To generate a bivariate(k=2) stationary VARMA(1,1) time series
![y_t - m{\mu} = \Phi ( y_{t-1} - m{\mu} ) +
m{\epsilon}_t - \Theta m{\epsilon}_{t-1},](images/i17eq418.gif)
with
,where
![\Sigma=[\matrix{1.0 & 0.5 \cr
0.5 & 1.25\cr
}],
\mu=[\matrix{10 \cr 20 \cr}],
...
... -0.5 \cr
0.6 & 0.3 \cr
}],
\Theta=[\matrix{-0.6 & 0.3 \cr
0.3 & 0.6 \cr
}],](images/i17eq420.gif)
you can specify
call varmasim(yt, phi, theta, mu, sigma, 100);
To generate a bivariate(k=2) nonstationary VARMA(1,1) time series
with the same mu, sigma, and theta in previous example
and the AR coefficient
![\Phi=[\matrix{1.0 & 0 \cr
0 & 0.3 \cr
}],](images/i17eq421.gif)
you can specify
call varmasim(yt, phi, theta, mu, sigma, 100) initial=3;
Copyright © 1999 by SAS Institute Inc., Cary, NC, USA. All rights reserved.