  Sequential methods for synthetic realisation of random processes have a
number of advantages compared with spectral methods. In this article, the
determination of optimal autoregressive (AR) models for reproducing a
predefined target autocovariance function of a random process is addressed. To
this end, a novel formulation of the problem is developed. This formulation is
linear and generalises the well-known Yule-Walker (Y-W) equations and a recent
approach based on restricted AR models (Krenk-Moller approach, K-M). Two main
features characterise the introduced formulation: (i) flexibility in the choice
for the autocovariance equations employed in the model determination, and (ii)
flexibility in the definition of the AR model scheme. Both features were
exploited by a genetic algorithm to obtain optimal AR models for the particular
case of synthetic generation of homogeneous stationary isotropic turbulence
time series. The obtained models improved those obtained with the Y-W and K-M
approaches for the same model parsimony in terms of the global fitting of the
target autocovariance function. Implications for the reproduced spectra are
also discussed. The formulation for the multivariate case is also presented,
highlighting the causes behind some computational bottlenecks.
