A Class of Method for Generating Correlating Uniform Variates

This paper introduces a class of methods called TES (Transform-Expand-Sample) for generating correlated variates with uniform marginals and Markovian structure. TES methods are readily implemented on a computer and have generation complexity comparable to that of the i.i.d. uniform sequence which they transform to a correlated uniform sequence. For any prescribed correlation coefficient rho, there is a TES method generating a uniform sequence with the 1-lag autocorrelation rho. Furthermore, the resultant correlation is monotone quadratic in two structural TES parameters.