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.

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