simGauss {longmemo}R Documentation

Simulate (Fractional) Gaussian Processes

Description

Simulation of a Gaussian series X(1), ..., X(n). Whereas simGauss works from autocovariances, the others call it, for simulating a fractional ARIMA(0,d,0) process (d = H-1/2), or fractional Gaussian noise, respectively.

Usage

simARMA0(n, H)
simFGN0 (n, H)
simGauss(autocov)

Arguments

n length of time series
H self-similarity parameter
autocov numeric vector of auto covariances gamma(0), ..., gamma(n-1).

Details

simGauss implements the method by Davies and Harte which is relatively fast using the FFT (fft) twice.

To simulate ARIMA(p, d, q), (for d in (-1/2, 1,2), you can use arima.sim(n, model = list(ar= .., ma = ..), innov= simARMA0(n,H=d+1/2) , n.start = 0).

Value

The simulated series X(1), ..., X(n), an R object of class "ts", constructed from ts().

Author(s)

Jan Beran (original) and Martin Maechler (simGauss, speedup, simplication)).

References

Beran (1994), 11.3.3, p.216~f, referring to

Davis, R.B. and Harte, D.S. (1987). Tests for Hurst effect, Biometrika 74, 95–102.

See Also

ckARMA0 on which simARMA0 relies, and ckFGN0 on which simFGN0 relies.

Examples

  x1 <- simFGN0(100, 0.7)
  x2 <- simARMA0(100, 0.7)
  plot(simFGN0(1000, 0.8)) #- time series plot

[Package longmemo version 0.9-6 Index]