ltsa (version 1.4.6)

DHSimulate: 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

n

length of time series to be generated

r

autocovariances at lags 0,1,...

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.

rand.gen

random number generator to use. It is assumed to have mean zero and variance one.

...

optional arguments passed to rand.gen

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.

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.

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.

See Also

\ DLSimulate , SimGLP, 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