# rSnorm: Simulation of a stationary Gaussian time series. In SuperGauss: Superfast Likelihood Inference for Stationary Gaussian Time Series

## Description

Simulation of a stationary Gaussian time series.

## Usage

 `1` ```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.

## 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.

## Value

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

## Examples

 ```1 2 3``` ```N <- 10 acf <- exp(-(1:N - 1)) rSnorm(n = 3, acf = acf) ```

SuperGauss documentation built on May 1, 2019, 7:58 p.m.