97-02-01.hau-wh
The Generation of Stationary Gaussian Time Series
Abstract
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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Wolfgang.Hoermann@statistik.wu-wien.ac.at