The k-factor GARMA Process with Infinite Variance Innovations

Abstract

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.

Keywords:

• Conditional sum squares
• Gegenbauer polynomial
• Long memory
• Markov chains Monte Carlo
• Stable distributions
• Whittle estimation.

Mathematics Subject Classification:

• 65C05; 62M10; 60G18

Notes

The boxplots of these parameters are not shown here but are available to authors upon request.

The boxplots for parameters in Tables 5–8 are available to authors upon request.