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