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Some extensions of linear approximation and prediction problems for stationary processes

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  • Ibragimov, Ildar
  • Kabluchko, Zakhar
  • Lifshits, Mikhail

Abstract

Let (B(t))t∈Θ with Θ=Z or Θ=R be a wide sense stationary process with discrete or continuous time. The classical linear prediction problem consists of finding an element in span¯{B(s),s≤t} providing the best possible mean square approximation to the variable B(τ) with τ>t.

Suggested Citation

  • Ibragimov, Ildar & Kabluchko, Zakhar & Lifshits, Mikhail, 2019. "Some extensions of linear approximation and prediction problems for stationary processes," Stochastic Processes and their Applications, Elsevier, vol. 129(8), pages 2758-2782.
    • Handle: RePEc:eee:spapps:v:129:y:2019:i:8:p:2758-2782
    DOI: 10.1016/j.spa.2018.08.001
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    References listed on IDEAS

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    1. Rosinski, Jan & Zak, Tomasz, 1996. "Simple conditions for mixing of infinitely divisible processes," Stochastic Processes and their Applications, Elsevier, vol. 61(2), pages 277-288, February.
    2. Hardin, Clyde D., 1982. "On the spectral representation of symmetric stable processes," Journal of Multivariate Analysis, Elsevier, vol. 12(3), pages 385-401, September.
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