Mixed Moving Averages and Self-Similarity

  • Vladas Pipiras
  • Murad S. Taqqu
Part of the SpringerBriefs in Probability and Mathematical Statistics book series (SBPMS )


The focus of the chapter is on a large class of symmetric stable self-similar processes with stationary increments, known as self-similar mixed moving averages. Minimal representations of self-similar mixed moving averages are related to nonsingular flows. Based on the structure of the underlying flows, self-similar mixed moving averages are decomposed uniquely into four major classes that are associated with dissipative, fixed, cyclic and conservative nonperiodic flows. These classes are also derived based on nonminimal representations, without referring to the underlying flows. Finally, canonical representations of self-similar mixed moving averages are derived for the dissipative, fixed and cyclic classes, and an example of a conservative nonperiodic self-similar mixed moving average is also provided.


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Copyright information

© The Author(s) 2017

Authors and Affiliations

  • Vladas Pipiras
    • 1
  • Murad S. Taqqu
    • 2
  1. 1.Statistics and Operations ResearchUniversity of North Carolina at Chapel HillChapel HillUSA
  2. 2.Department of Mathematics and StatisticsBoston UniversityBostonUSA

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