Matrix products for the synthesis of stationary time series with a priori prescribed joint distributions

摘要

Inspired from non-equilibrium statistical physics models, a general frameworkenabling the definition and synthesis of stationary time series with a prioriprescribed and controlled joint distributions is constructed. Its centralfeature consists of preserving for the joint distribution the simple productstruc- ture it has under independence while enabling to input con- trolled andprescribed dependencies amongst samples. To that end, it is based on productsof d-dimensional matrices, whose entries consist of valid distributions. Thestatistical properties of the thus defined time series are studied in details.Having been able to recast this framework into that of Hidden Markov Modelsenabled us to obtain an efficient synthesis procedure. Pedagogical well-chosenexamples (time series with the same marginal distribution, same covariancefunction, but different joint distributions) aim at illustrating the power andpotential of the approach and at showing how targeted statistical prop- ertiescan be actually prescribed.