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.