LoglikelihoodAR: Exact Loglikelihood for AR
In FitAR: Subset AR Model Fitting

Description Usage Arguments Details Value Warning Note Author(s) References See Also Examples

The exact loglikelihood function, defined in eqn. (6) of McLeod & Zhang (2006) is computed. Requires O(n) flops, n = length(z).

1	LoglikelihoodAR(phi, z, MeanValue = 0)

`phi`	AR parameters
`z`	time series data, not assumed mean corrected
`MeanValue`	usually this is mean(z) but it could be another value for example the MLE of the mean

Eqn (6) of McLeod and Zhang (2006) may be written

-(n/2) \log(\hatσ_a^2) - (1/2) \log(g_p),

where \hatσ_a^2 is the residual variance and g_p is the covariance determinant.

The value of the loglikelihood is returned

No check is done for stationary-causal process

For MLE computation it is better to use FastLoglikelihoodAR since for repeated likelihood evaluations this requires only O(1) flops vs O(n) flops, where n = length(z).

A.I. McLeod and Y. Zhang

McLeod, A.I. and Zhang, Y. (2006). Partial autocorrelation parameterization for subset autoregression. Journal of Time Series Analysis, 27, 599-612.

FastLoglikelihoodAR

#Fit a subset model to Series A and verify the loglikelihood
 out<-FitAR(SeriesA, c(1,2,7))
 out
#either using print.default(out) to see the components in out
#or applying LoglikelihoodAR () by first obtaining the phi parameters as out$phiHat.

#
 LoglikelihoodAR(out$phiHat, SeriesA, MeanValue=mean(SeriesA))