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Further comments on the representation problem for stationary processes

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  • Laurent, Stéphane

Abstract

We comment on some points about the coding of stochastic processes by sequences of independent random variables. The most interesting question has to do with the standardness property of the filtration generated by the process, in the framework of Vershik's theory of filtrations. Non-standardness indicates the presence of long memory in a purely probabilistic sense. We aim to provide a short, non-technical presentation of Vershik's theory of filtrations.

Suggested Citation

  • Laurent, Stéphane, 2010. "Further comments on the representation problem for stationary processes," Statistics & Probability Letters, Elsevier, vol. 80(7-8), pages 592-596, April.
    • Handle: RePEc:eee:stapro:v:80:y:2010:i:7-8:p:592-596
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    References listed on IDEAS

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    1. Rosenblatt, M., 2009. "A comment on a conjecture of N. Wiener," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 347-348, February.
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