Algorithmic modeling of TES processes

TES (transform-expand-sample) is a versatile class of stationary stochastic processes which can model arbitrary marginals, a wide variety of autocorrelation functions, and a broad range of sample path behaviors. TES parameters are of two kinds: the first kind is used for the exact fitting of the empirical distribution (histogram), while the second kind is used for approximating the empirical autocorrelation function. Parameters of the first kind are easy to determine algorithmically, but those of the second kind require a hard heuristic search on a large parametric function space. This paper describes an algorithmic procedure which can replace the heuristic search, thereby largely automating TES modeling. The algorithm is cast in nonlinear programming setting with the objective of minimizing a weighted sum of squared differences between the empirical autocorrelations and their candidate TES model counterparts. It combines a brute-forte search with steepest-descent nonlinear programming using Zoutendijk´s feasible direction method. Finally, we illustrate the efficacy of our approach via three examples: two from the domain of VBR (variable bit rate) compressed video and one representing results from a laser intensity experiment.