Using surrogates and optimal transport for synthesis of stationary multivariate series with prescribed covariance function and non-gaussian joint-distribution

Surrogates are investigated as procedures of synthesis for multi-variate time series with prescribed properties. First it is shown how to prescribe a multivariate covariance function jointly with the (possibly non-Gaussian) marginal distributions. Second, using histogram matching by approximate optimal transport with the Sliced Wasserstein Distance, the surrogate synthesis is extended to prescribe covariance function and joint-distribution of the components. Algorithms are described and justified, and numerical examples are shown. MATLAB codes are publicly available online.