The Generation of Stationary Gaussian Time Series

Three di erent algorithms for the generation of stationary Gaussian time series with given autocorrelation function are presented in this paper. The algorithms have already been suggested in the literature but are not well known and have never been compared before. Interrelations between the di erent methods, advantages and disadvantages with respect to speed and memory requirements and the range of autocorrelation functions for which the di erent methods are stable are discussed. The time-complexity of the algorithms and the comparisons of their implementations show that the method twice using the Fourier transform is by far the most e cient if time series of moderate or large length are generated. A tested C-code of the latter algorithm is included as this method is tricky to implement and very di cult to nd in the literature. (We know only one reference, that gives a correct algorithm, but there the description is very short and no proof is included.)