# zbMATH — the first resource for mathematics

TES: A class of methods for generating autocorrelated uniform variates. (English) Zbl 0764.65002
This paper introduces a new class of simple generation methods for Markovian sequences of random variables with uniform marginals, called transform-expand-sample (TES). A basic TES method is a nonlinear autoregressive scheme with modulo-1 arithmetic; each is determined by a transformation and two parameters $$\alpha\in[0,1]$$ and $$\varphi\in[- 1,1]$$.
The first autocorrelation of TES sequences is analytically computed and it is shown that, for two fundamental TES methods, the resulting lag-1 autocorrelation $$\rho_ 1$$ as a function of $$\alpha$$ and $$\varphi$$ spans every values in $$(-1,1)$$ and is monotonic quadratic in both $$\alpha$$ and $$\varphi$$.
On the other hand, higher autocorrelations are investigated empirically by simulation. The sample paths of TES are cyclical and exhibit discontinuity in the neighborhood of point 0 due to wraparound. So, transformations of TES methods are presented to make the sample paths more continuous-looking while preserving their marginal uniformity.
Reviewer: K.Uosaki (Tottori)

##### MSC:
 65C10 Random number generation in numerical analysis
Full Text: