# Stochastic synthesis approximating any process dependence and distribution

## Abstract

An extension of the symmetric-moving-average (SMA) scheme is presented for stochastic synthesis of a stationary process for approximating any dependence structure and marginal distribution. The extended SMA model can exactly preserve an arbitrary second-order structure as well as the high order moments of a process, thus enabling a better approximation of any type of dependence (through the second-order statistics) and marginal distribution function (through statistical moments), respectively. Interestingly, by explicitly preserving the coefficient of kurtosis, it can also simulate certain aspects of intermittency, often characterizing the geophysical processes. Several applications with alternative hypothetical marginal distributions, as well as with real world processes, such as precipitation, wind speed and grid-turbulence, highlight the scheme’s wide range of applicability in stochastic generation and Monte-Carlo analysis. Particular emphasis is given on turbulence, in an attempt to simulate in a simple way several of its characteristics regarded as puzzles.

## Keywords

Stochastic modelling Grid-turbulence Hourly surface wind speed Daily precipitation Intermittency Kumaraswamy distribution Normal-inverse-Gaussian distribution## Notes

### Acknowledgements

The Authors are grateful to the Editor George Christakos, the anonymous Associate Editor and three Reviewers as well as to T. Iliopoulou, for their efforts, useful comments and suggestions that helped us improve the paper.

## References

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