Description Usage Arguments Value Author(s) References Examples

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

1 | ```
hosking.sim(n, acvs)
``` |

`n` |
Length of series. |

`acvs` |
Autocovariance sequence of series with which to generate,
must be of length at least |

Length `n`

time series from true autocovariance sequence
`acvs`

.

Brandon Whitcher

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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 | ```
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)
## End(Not run)
``` |

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