ltsa (version 1.4.2)

exactLoglikelihood: Exact log-likelihood and MLE for variance

Description

Provides an exact log-likelihood that is exactly equal to the value of the probability density function with the random variables replaced by data and the parameters replaced by their estimated value. The corresponding estimate of the variance term is return.

Usage

exactLoglikelihood(r, z, innovationVarianceQ = TRUE)

Arguments

r

the portion of autocovariance function which when multiplied by the variance term equals the full autocovariance function.

z

the time series assumed to have mean zero

innovationVarianceQ

When TRUE, the variance term is the innovation variance and when FALSE it is the variance of the time series.

Value

• LL
  exact log-likelihood
• sigmaSq
  MLE for the variance term

Details

This function uses the trench algorithm that is implememented in C to comp

See Also

TrenchLoglikelihood

Examples

set.seed(7773311)
n <- 200
z <- arima.sim(model=list(ar=0.9, ma=-0.6), n=n, n.start=10^4)
out <- arima(z, order=c(1,0,1), include.mean=FALSE)
out
#note
#sigma^2 estimated as 0.9558:  log likelihood = -279.66,  aic = 565.31
r <- tacvfARMA(phi=coef(out)[1], theta=-coef(out)[2], maxLag=n-1)
exactLoglikelihood(r, z, innovationVarianceQ = TRUE)
#agrees!