The k-factor GARMA Process with Infinite Variance Innovations

In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. ( 2008 ). Sta...

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Bibliographic Details
Published in:Communications in statistics. Simulation and computation 2016-02, Vol.45 (2), p.420-437
Main Authors: Diongue, Abdou Kâ, Ndongo, Mor
Format: Article
Language:English
Subjects:
65C05
62M10
60G18
Computer simulation
Conditional sum squares
Gegenbauer polynomial
Long memory
Markov chains Monte Carlo
Mathematical analysis
Monte Carlo methods
Rivers
Samples
Stable distributions
Statistical analysis
Variance
Water runoff
Whittle estimation
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Summary:In this article, we develop the theory of k-factor Gegenbauer Autoregressive Moving Average (GARMA) process with infinite variance innovations which is a generalization of the stable seasonal fractional Autoregressive Integrated Moving Average (ARIMA) model introduced by Diongue et al. ( 2008 ). Stationarity and invertibility conditions of this new model are derived. Conditional Sum of Squares (CSS) and Markov Chains Monte Carlo (MCMC) Whittle methods are investigated for parameter estimation. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques. Finally, the usefulness of the model is corroborated with the application to streamflow data for Senegal River at Bakel.
ISSN:0361-0918
1532-4141
DOI:10.1080/03610918.2013.824095