Existence and construction of translation models for stationary non-Gaussian processes

Abstract

Translation models are memoryless transformations of Gaussian processes specified by their marginal distribution F and covariance function ξ . Iteration schemes are commonly used to find probability laws of Gaussian images of translation models, although these schemes may not converge since translation models do not exist for arbitrary functions F and ξ . Pairs ( F , ξ ) for which translation models exist are said to be consistent. Optimization algorithms are developed for constructing translation models that, for consistent pairs ( F , ξ ) , match F and ξ , and, for inconsistent pairs ( F , ξ ) , match F or ξ and approximate ξ or F . The resulting translation models can be used in Monte Carlo simulation studies.