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Parameter estimation for Gegenbaeur Arfisma processes with infinite variance innovations

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  • Filamory Abraham Michael Keïta
  • Ouagnina Hili
  • Serge-Hippolyte Arnaud Kanga

Abstract

In this study, we consider the Gegenbauer ARFISMA process with α-stable innovations which belong to the class of infinite variance time series. This is a finite parameter model that exhibits long-range dependence, high variability, and Seasonal and /or Cyclical Long Memory (SCLM) variations. The Gegenbauer ARFISMA time series with α-stable innovations can be rewritten as linear processes (infinite order moving averages) with coefficients that decay slowly to zero and with innovations that are in the domain of attraction of a α-stable distribution with stability parameter (1

Suggested Citation

  • Filamory Abraham Michael Keïta & Ouagnina Hili & Serge-Hippolyte Arnaud Kanga, 2025. "Parameter estimation for Gegenbaeur Arfisma processes with infinite variance innovations," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 54(1), pages 204-229, January.
    • Handle: RePEc:taf:lstaxx:v:54:y:2025:i:1:p:204-229
    DOI: 10.1080/03610926.2024.2307453
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