rnormtz {SuperGauss}

Simulate a stationary Gaussian time series.

Description

Simulate a stationary Gaussian time series.

Usage

rnormtz(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 ⁠O(N log N)⁠ FFT-based algorithm of Wood and Chan (1994) or the more stable O(N^2) 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.

Details

The FFT method fails when the embedding circulant matrix is not positive definite. This is typically due to one of two things:

1. Roundoff error can make tiny eigenvalues appear negative. For this purpose, argument tol can be used to replace all negative eigenvalues by tol * ev_max, where ev_max is the largest eigenvalue.

2. The autocorrelation is decaying too slowly on the given timescale. To mitigate this, argument nkeep can be used to supply a longer acf than is required, and keep only the first nkeep time series observations. For consistency, nkeep also applies to Durbin-Levinson method.

Value

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

Examples

N <- 10
acf <- exp(-(1:N - 1)/N)
rnormtz(n = 3, acf = acf)