varmares

Purpose

Computes residuals of a Vector ARMA model.

Format

res = varmares(w, phi, theta)

Parameters:

• w (NxK matrix) – time series.
• phi ((K*P)xK matrix) – AR coefficient matrices.
• theta ((K*Q)xK matrix) – MA coefficient matrices.

Returns:

res (NxK matrix) –

residuals. If the calculation fails res is set to missing value with error code:

Error Code	Reason for Failure
1	\(M < 1\)
2	\(N < 1\)
3	\(P < 0\)
4	\(Q < 0\)
5	\(P = 0\) and \(Q = 0\)
7	floating point work space too small
8	integer work space too small
10	AR parameters too close to stationarity boundary
11	model not stationary
12	model not invertible
13	\(I+M'H'HM\) not positive definite

Remarks

varmares() is adapted from code developed by Jose Alberto Mauricio of the Universidad Complutense de Madrid. It was published as Algorithm AS311 in Applied Statistics. Also described in “Exact Maximum Likelihood Estimation of Stationary Vector ARMA Models,” JASA, 90:282-264.