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

DHSimulate.Rd

```
\name{DHSimulate}
\alias{DHSimulate}
\title{ Simulate General Linear Process }
\description{
Uses the Davies-Harte algorithm to simulate a Gaussian time
series with specified autocovariance function.
}
\usage{
DHSimulate(n, r, ReportTestOnly = FALSE, rand.gen = rnorm, ...)
}
\arguments{
\item{n}{ length of time series to be generated }
\item{r}{ autocovariances at lags 0,1,...}
\item{ReportTestOnly}{ FALSE -- Run normally so terminates with an error if Davies-Harte condition
does not hold. Othewise if TRUE, then output is TRUE if the Davies-Harte condition holds
and FALSE if it does not.}
\item{rand.gen}{ random number generator to use. It is assumed to have mean zero and
variance one.}
\item{\dots}{optional arguments passed to \code{rand.gen} }
}
\details{
The method uses the FFT and so is most efficient if the series length, n,
is a power of 2.
The method requires that a complicated non-negativity condition be satisfed.
Craigmile (2003) discusses this condition in more detail and shows for
anti-persistent time series this condition will always be satisfied.
Sometimes, as in the case of fractinally differenced white noise with
parameter d=0.45 and n=5000, this condition fails and the algorithm doesn't
work.
In this case, an error message is generated and the function halts.
}
\value{
Either a vector of length containing the simulated time series if Davies-Harte condition
holds and ReportTestOnly = FALSE.
If argument ReportTestOnly is set to TRUE, then output is logical variable indicating
if Davies-Harte condition holds, TRUE, or if it does not, FALSE.
}
\author{ A.I. McLeod}
\references{
Craigmile, P.F. (2003).
Simulating a class of stationary Gaussian processes using the Davies-Harte algorithm,
with application to long memory processes.
Journal of Time Series Analysis, 24, 505-511.
Davies, R. B. and Harte, D. S. (1987).
Tests for Hurst Effect. Biometrika 74, 95--101.
McLeod, A.I., Yu, Hao, Krougly, Zinovi L. (2007).
Algorithms for Linear Time Series Analysis,
Journal of Statistical Software.
}
\seealso{ \
\code{\link{DLSimulate}} ,
\code{\link{SimGLP}},
\code{\link{arima.sim}}
}
\examples{
#simulate a process with autocovariance function 1/(k+1), k=0,1,...
# and plot it
n<-2000
r<-1/sqrt(1:n)
z<-DHSimulate(n, r)
plot.ts(z)
#simulate AR(1) and produce a table comparing the theoretical and sample
# autocovariances and autocorrelations
phi<- -0.8
n<-4096
g0<-1/(1-phi^2)
#theoretical autocovariances
tacvf<-g0*(phi^(0:(n-1)))
z<-DHSimulate(n, tacvf)
#autocorrelations
sacf<-acf(z, plot=FALSE)$acf
#autocovariances
sacvf<-acf(z, plot=FALSE,type="covariance")$acf
tacf<-tacvf/tacvf[1]
tb<-matrix(c(tacvf[1:10],sacvf[1:10],tacf[1:10],sacf[1:10]),ncol=4)
dimnames(tb)<-list(0:9, c("Tacvf","Sacvf","Tacf","Sacf"))
tb
#Show the Davies-Harte condition sometimes hold and sometimes does not
# in the case of fractionally differenced white noise
#
#Define autocovariance function for fractionally differenced white noise
`tacvfFdwn` <-
function(d, maxlag)
{
x <- numeric(maxlag + 1)
x[1] <- gamma(1 - 2 * d)/gamma(1 - d)^2
for(i in 1:maxlag)
x[i + 1] <- ((i - 1 + d)/(i - d)) * x[i]
x
}
#Build table to show values of d for which condition is TRUE when n=5000
n<-5000
ds<-c(-0.45, -0.25, -0.05, 0.05, 0.25, 0.45)
tb<-logical(length(ds))
names(tb)<-ds
for (kd in 1:length(ds)){
d<-ds[kd]
r<-tacvfFdwn(d, n-1)
tb[kd]<-DHSimulate(n, r, ReportTestOnly = TRUE)
}
tb
}
\keyword{ ts }
\keyword{ datagen }
```

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