SuperGauss (version 1.0.2)

rSnorm: Simulation of a stationary Gaussian time series.

Description

Simulation of a stationary Gaussian time series.

Usage

rSnorm(n = 1, acf, Z, fft = TRUE, nkeep, tol = 1e-06)

Arguments

n

Number of time series to generate.

acf

Length-N vector giving the autocorrelation of the series.

Z

Optional size (2N-2) x n or N x n matrix of iid standard normals, to use in the fft and Durbin-Levinson methods respectively.

fft

Logical, whether or not to use the superfast FFT-based algorithm of Chan and Wood or the more stable Durbin-Levinson algorithm. See Details.

nkeep

Length of time series. Defaults to N = length(acf). See Details.

tol

Relative tolerance on negative eigenvalues. See Details.

Value

Length-nkeep vector or size nkeep x n matrix with time series as columns.

Details

The superfast method fails when the circulant matrix is not positive definite. This is typically due to one of two things, for which the FFT algorithm can be tuned with tol and nkeep:

tol

Roundoff error can make tiny eigenvalues appear negative. If evMax is the maximum eigenvalue, then all negative eigenvalues of magnitude less than tol * evMax are mapped to this threshold value. This does not guarantee a positive definite embedding.

nkeep

The autocorrelation is decaying too slowly on the given timescale. To mitigate this it is possible to increase the time horizon, i.e. input a longer acf and keep the first nkeep time series observations. For consistency, nkeep also applies to Durbin-Levinson method.

Examples

# NOT RUN {
N <- 10
acf <- exp(-(1:N - 1))
rSnorm(n = 3, acf = acf)
# }