Parameter estimation for Gegenbaeur Arfisma processes with infinite variance innovations

Filamory Abraham Michael Keïta, Ouagnina Hili and Serge-Hippolyte Arnaud Kanga

Communications in Statistics - Theory and Methods, 2025, vol. 54, issue 1, 204-229

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

Date: 2025
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DOI: 10.1080/03610926.2024.2307453

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