Revision 0a03bbb7cf19e479dc77592ed09621eeb8afb470 authored by A.I. McLeod on 21 December 2015, 08:55:04 UTC, committed by cran-robot on 21 December 2015, 08:55:04 UTC
1 parent 83deceb
PredictionVariance.Rd
\name{PredictionVariance}
\alias{PredictionVariance}
\title{ Prediction variance}
\description{
is computed given theoretical autocovariances.
}
\usage{
PredictionVariance(r, maxLead = 1, DLQ = TRUE)
}

\arguments{
\item{r}{ the autocovariances at lags 0, 1, 2, ... }
\item{DLQ}{ Using Durbin-Levinson if TRUE. Otherwise Trench algorithm used. }
}

\details{
Two algorithms are available which
are described in detail in McLeod, Yu and Krougly (2007).
The default method, DLQ=TRUE, uses the autocovariances provided in r to
determine the optimal linear mean-square error predictor of order
length(r)-1.
The mean-square error of this predictor is the lead-one error variance.
The moving-average expansion of this model is used to compute any
remaining variances (McLeod, Yu and Krougly, 2007).
With the other Trench algorithm, when DLQ=FALSE, a direct matrix representation
of the forecast variances is used (McLeod, Yu and Krougly, 2007).
The Trench method is exact.  Provided the length of r is large enough,
the two methods will agree.
}

\value{
vector of length maxLead containing the variances
}

\references{
McLeod, A.I., Yu, Hao, Krougly, Zinovi L.  (2007).
Algorithms for Linear Time Series Analysis,
Journal of Statistical Software.
}

\author{ A.I. McLeod }

\seealso{
}

\examples{
#Example 1. Compare using DL method or Trench method
cbind(va,vb)
#
#Example 2. Compare with predict.Arima
#general script, just change z, p, q, ML
z<-sqrt(sunspot.year)
n<-length(z)
p<-9
q<-0
ML<-10
#for different data/model just reset above
out<-arima(z, order=c(p,0,q))
sda<-as.vector(predict(out, n.ahead=ML)$se) # phi<-theta<-numeric(0) if (p>0) phi<-coef(out)[1:p] if (q>0) theta<-coef(out)[(p+1):(p+q)] zm<-coef(out)[p+q+1] sigma2<-out$sigma2
r<-sigma2*tacvfARMA(phi, theta, maxLag=n+ML-1)
cbind(sda,sdb)
#
#
#Example 3. DL and Trench method can give different results
#  when the acvf is slowly decaying. Trench is always
#  exact based on a finite-sample.
L<-5
r<-1/sqrt(1:(L+1))