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Abstract: A fast and exact procedure for the numerical synthesis of stationary multivariate Gaussian time series with a priori prescribed and well controlled auto- and cross-covariance functions is proposed. It is based on extending the circulant embedding technique to the multivariate case and can be viewed as a modification and variation around the Chan and Wood algorithm proposed earlier to solve the same problem. The procedure is shown to yield time series possessing exactly the desired covariance structure, when sufficient conditions are satisfied. Such conditions are discussed theoretically and examined on several examples of multivariate time series models. Issues related to prescribing a priori the spectral structure rather than the covariance one are also discussed. Matlab routines implementing this procedure are publicly available at http://www.hermir.org. [Copyright &y& Elsevier]

Assessing world-wide financial integration constitutes a recurrent challenge in macroeconometrics, often addressed by visual inspections searching for data patterns. Econophysics literature enables us to build complementary, data-driven measures of financial integration using graphs. The present contribution investigates the potential and interests of a novel 3-step approach that combines several state-of-the-art procedures to (i) compute graph-based representations of the multivariate dependence structure of asset prices time series representing the financial states of 32 countries world-wide (1955–2015); (ii) compute time series of 5 graph-based indices that characterize the time evolution of the topologies of the graph; (iii) segment these time evolutions in piece-wise constant eras, using an optimization framework constructed on a multivariate multi-norm total variation penalized functional. The method shows first that it is possible to find endogenous stable eras of world-wide financial integration. Then, our results suggest that the most relevant globalization eras would be based on the historical patterns of global capital flows, while the major regulatory events of the 1970s would only appear as a cause of sub-segmentation. [ABSTRACT FROM AUTHOR]