The Generation of Stationary Gaussian Time Series

Michael A. Hauser and Wolfgang Hörmann


Three different 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 different methods, advantages and disadvantages with respect to speed and memory requirements and the range of autocorrelation functions for which the different 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 efficient 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 difficult to find 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.)

Mathematics Subject Classification: 65C10 (Random Number Generation)

CR Categories and Subject Descriptors: G.3 [Probability and Statistics]: Random number generation

Key Words: random number generation, Cholesky decomposition, Durbin algorithm, fast Fourier transform, fractionally integrated processes

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