waveslim (version 1.7.5)

# hosking.sim: Generate Stationary Gaussian Process Using Hosking's Method

## Description

Uses exact time-domain method from Hosking (1984) to generate a simulated time series from a specified autocovariance sequence.

## Usage

`hosking.sim(n, acvs)`

## Arguments

n

Length of series.

acvs

Autocovariance sequence of series with which to generate, must be of length at least `n`.

## Value

Length `n` time series from true autocovariance sequence `acvs`.

## References

Hosking, J. R. M. (1984) Modeling persistence in hydrological time series using fractional differencing, Water Resources Research, 20, No. 12, 1898-1908.

Percival, D. B. (1992) Simulating Gaussian random processes with specified spectra, Computing Science and Statistics, 22, 534-538.

## Examples

```# NOT RUN {
dB <- function(x) 10 * log10(x)
per <- function (z) {
n <- length(z)
(Mod(fft(z))^2/(2 * pi * n))[1:(n%/%2 + 1)]
}
spp.sdf <- function(freq, delta, omega)
abs(2 * (cos(2*pi*freq) - cos(2*pi*omega)))^(-2*delta)
data(acvs.andel8)
n <- 1024
# }
# NOT RUN {
z <- hosking.sim(n, acvs.andel8[,2])
per.z <- 2 * pi * per(z)
par(mfrow=c(2,1), las=1)
plot.ts(z, ylab="", main="Realization of a Seasonal Long-Memory Process")
plot(0:(n/2)/n, dB(per.z), type="l", xlab="Frequency", ylab="dB",
main="Periodogram")
lines(0:(n/2)/n, dB(spp.sdf(0:(n/2)/n, .4, 1/12)), col=2)
# }
```