Spectral analysis of basic Transform-Expand Sample processes

This paper studies the spectral properties of a class of stochastic sequences generated by basic TES (Transform-Expand-Sample) methods, as well as transformed TES sequences. A TES sequence is obtained as a marginally uniform process from an autoregressive scheme with modulo-1 reduction, followed by additional transformations. We derive formulae for the spectral density function and the spectral distribution function which are suitable for efficient numerical computation. A set of examples is calculated and exhibited for TES processes with uniform and exponential marginals. The results contribute to the understanding of TES sequences as models of autocorrelated sequences, particularly in a Monte Carlo simulation context.