varmall

Purpose

Computes log-likelihood of a Vector ARMA model.

Format

ll = varmall(w, phi, theta, vc)
Parameters:
  • w (NxK matrix) – time series.
  • phi ((K*P)xK matrix) – AR coefficient matrices.
  • theta ((K*Q)xK matrix) – MA coefficient matrices.
  • vc (KxK matrix) – covariance matrix.
Returns:

ll (scalar) –

log-likelihood. If the calculation fails ll 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
9 vc is not positive definite
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

varmall() 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.