The transition and autocorrelation structure of tes processes: Part II: Special cases

David L. Jagerman, Benjamin Melamed

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TES (Transform-Expand-Sample) is a versatile class of stochastic sequences which can capture arbitrary marginals and a wide variety of sample path behavior and autocorrelation functions. In TES, the initial variate is uniform on [0,1) and the next variate is obtained recursively by taking the fractional part (i.e., modulo-1 reduction) of a linear autoregressive scheme. The uniform TES variates can then be further transformed to have arbitrary marginals. A companion paper (Part I) presented the general theory of TES processes. This paper (Part II) contains various examples which demonstrate the efficacy of the TES paradigm by comparing numerical and simulation-based calculations for a variety of TES autocorrelation functions. The results have applications to the modeling of autocorrelated sequences, particularly in a Monte Carlo simulation context.

Original languageEnglish (US)
Pages (from-to)499-527
Number of pages29
JournalStochastic Models
Issue number3
StatePublished - 1992
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Modeling and Simulation


  • Markov processes
  • Monte Carlo simulation
  • TES Processes and Methods
  • autocorrelated variates
  • autocorrelation function
  • autocovariance function
  • autoregressive processes
  • correlated variates


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