Simulation of Stochastic Processes Exhibiting Any‐Range Dependence and Arbitrary Marginal Distributions

Abstract

AbstractHydrometeorological processes are typically characterized by temporal dependence, short‐ or long‐range (e.g., Hurst behavior), as well as by non‐Gaussian distributions (especially at fine time scales). The generation of long synthetic time series that resembles the marginal and joint properties of the observed ones is a prerequisite in many uncertainty‐related hydrological studies, since they can be used as inputs and hence allow the propagation of natural variability and uncertainty to the typically deterministic water‐system models. For this reason, it has been for years one of the main research topics in the field of stochastic hydrology. This work presents a novel model for synthetic time series generation, termed Symmetric Moving Average (neaRly) To Anything, that holds out the promise of simulating stationary univariate and multivariate processes with any‐range dependence and arbitrary marginal distributions, provided that the former is feasible and the latter have finite variance. This is accomplished by utilizing a mapping procedure in combination with the relationship that exists between the correlation coefficients of an auxiliary Gaussian process and a non‐Gaussian one, formalized through the Nataf's joint distribution model. The generality of Symmetric Moving Average (neaRly) To Anything is stressed through two hypothetical simulation studies (univariate and multivariate), characterized by different dependencies and distributions. Furthermore, we demonstrate the practical aspects of the proposed model through two real‐world cases, one that concerns the generation of annual non‐Gaussian streamflow time series at four stations and another that involves the synthesis of intermittent, non‐Gaussian, daily rainfall series at a single location.