Computes log-likelihood of a Vector ARMA model.
varmall(w, phi, theta, vc)¶
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.
ll (scalar) –
log-likelihood. If the calculation fails ll is set to missing value with error code:
Reason for Failure
\(M < 1\)
\(N < 1\)
\(P < 0\)
\(Q < 0\)
\(P = 0\) and \(Q = 0\)
floating point work space too small
integer work space too small
vc is not positive definite
AR parameters too close to stationarity boundary
model not stationary
model not invertible
\(I+M'H'HM\) not positive definite
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.