# hosking.sim: Generate Stationary Gaussian Process Using Hosking's Method In waveslim: Basic wavelet routines for one-, two- and three-dimensional signal processing

## Description

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

## Usage

 `1` ```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`.

Brandon Whitcher

## 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

 ``` 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) ```

waveslim documentation built on May 29, 2017, 3:23 p.m.