Stochastic Periodic Autoregressive to Anything (SPARTA): Modeling and Simulation of Cyclostationary Processes With Arbitrary Marginal Distributions

Abstract

Stochastic models in hydrology traditionally aim at reproducing the empirically derived statistical characteristics of the observed data rather than any specific distribution model that attempts to describe the usually non-Gaussian statistical behavior of the associated processes. SPARTA (Stochastic Periodic AutoRegressive To Anything) offers an alternative and novel approach which allows the explicit representation of each process of interest with any distribution model, while simultaneously establishes dependence patterns that cannot be fully captured by the typical linear stochastic schemes. Cornerstone of the proposed approach is the Nataf joint-distribution model, which is related with the Gaussian copula, combined with Gaussian periodic autoregressive processes. In order to obtain the target stochastic structure, we have also developed a computationally simple and efficient algorithm, based on a hybrid Monte-Carlo procedure that is used to approximate the required equivalent correlation coefficients. Theoretical and practical benefits of the proposed method, contrasted to outcomes from widely used stochastic models, are demonstrated by means of real-world as well as hypothetical monthly simulation examples involving both univariate and multivariate time series.