anySim-package: anySim: Stochastic Simulation of Processes with any Marginal...

In itsoukal/anySim: Stochastic Simulation of Processes with any Marginal Distribution and Correlation Structure

Description

anySim is an R package for the stochastic simulation of processes with any marginal distribution and dependence structure. Currently, the package provides models for the simulation of univariate stationary and cyclostationary processes, exhibiting continuous, discrete and mixed-type marginal distributions as well as any valid (i.e., positive definite) short-range or long-range autocorrelation structure. Furthermore, it implements a multivariate stationary stochastic model with similar capabilities, preserving also the lag-0 cross-correlation coefficients among the processes. The package can be used for the generation of synthetic time series (e.g., rainfall, runoff, temperature, wind speed etc.) with the desired marginal and stochastic properties.

Details

The methodology is based on the concept of Nataf’s joint distribution model (Nataf, 1962; Liu and Der Kiureghian 1986) according to which the joint distribution of random variables with any target arbitrary marginal distributions can be obtained by mapping an auxiliary multivariate standard Gaussian distribution via the inverse cumulative distribution functions (ICDFs). It exploits the link that exists between correlation coefficients in the Gaussian and the target domain, reproducing also the target correlations. Moving to stochastic process simulation, anySim employs a similar concept (for more details see, Kossieris et al., 2019; Tsoukalas et al., 2017, 2018a, 2018b, 2018c, 2019; Tsoukalas 2018) that is based on the mapping (through the ICDF) of an auxiliary Gaussian process (Gp) through the ICDF in order to establish processes with the target marginal distribution and correlation structure. The package comprises the following stochastic simulation models:

• Autoregressive To Anything model of order p - ARTA(p): This model uses an appropriately parameterised univariate AR(p) to simulate an auxiliary Gp to establish the target correlation structure. It is noted that a similar low-order (p=1) model has been proposed by Cario and Nelson (1996).

• Symmetric Moving Average To Anything - SMARTA(q): This model uses an appropriately parameterised SMA(q) model to simulate an auxiliary Gp to establish the target correlation structure. In the final step, the Gp realisation is mapped to the actual domain through the ICDF of the target distribution (Tsoukalas et al., 2018b, 2019; Tsoukalas, 2018).

• Stochastic Periodic Autoregressive To Anything model of order 1 - SPARTA: This model uses an appropriately parameterised univariate PAR(1) model to simulate a cyclostationary auxiliary Gp to establish the target season-to-season correlation structure (Tsoukalas et al., 2017, 2018a, 2019; Tsoukalas, 2018).

Author(s)

Developed by: Ioannis Tsoukalas [e-mail]
Panagiotis Kossieris [e-mail]

References

• Cario, M., and Nelson, B., 1996. Autoregressive to anything: Time-series input processes for simulation. Operations Research Letters, 19(2), 51–58. (link)

• Kossieris, P., Tsoukalas, I., Makropoulos, C., and Savic D., 2019. Simulating marginal and dependence behaviour of water demand processes at any fine time scale, Water, 11(5), 885.(link)

• Liu, P., and Der Kiureghian, A., 1986. Multivariate distribution models with prescribed marginals and covariances. Probabilistic Engineering Mechanics, 1(2), 105–112. (link)

• Nataf, A., 1962. Statistique mathematique-determination des distributions de probabilites dont les marges sont donnees. Comptes Rendus de l’Academie Des Sciences, 255(1), 42–43.

• Papalexiou, S., 2018. Unified theory for stochastic modelling of hydroclimatic processes: Preserving marginal distributions, correlation structures, and intermittency. Advances in Water Resources. (link)

• Tsoukalas, I., Efstratiadis, A., and Makropoulos, C., 2017. Stochastic simulation of periodic processes with arbitrary marginal distributions. 15th International Conference on Environmental Science and Technology (CEST2017), Rhodes, Greece. (link)

• Tsoukalas, I., Efstratiadis, A., and Makropoulos, C., 2018a. Stochastic periodic autoregressive to anything (SPARTA): Modeling and simulation of cyclostationary processes with arbitrary marginal distributions. Water Resources Research 54 (1), 161-185. (link)

• Tsoukalas, I., Makropoulos, C., and Koutsoyiannis, D., 2018b. Simulation of Stochastic Processes Exhibiting Any-Range Dependence and Arbitrary Marginal Distributions. Water Resources Research 54(11), 9484-9513. (link)

• Tsoukalas, I., Papalexiou, S.M, Efstratiadis, A., and Makropoulos, C., 2018c. A cautionary note on the reproduction of dependencies through linear stochastic models with non-Gaussian white noise. Water 10 (6), 771. (link)

• Tsoukalas, I., Efstratiadis, A., and Makropoulos, C., 2019. Building a puzzle to solve a riddle: A multi-scale disaggregation approach for multivariate stochastic processes with any marginal distribution and correlation structure. Journal of hydrology. (link).

• Tsoukalas, I., 2019. Modelling and simulation of non-Gaussian stochastic processes for optimization of water-systems under uncertainty, PhD thesis, 339 pages, National Technical University of Athens, December 2018. (link)

itsoukal/anySim documentation built on May 7, 2020, 11:57 p.m.