Estimation for seasonal fractional ARIMA with stable innovations via the empirical characteristic function method

Abstract

Seasonal fractional ARIMA (ARFISMA) model with infinite variance innovations is used in the analysis of seasonal long-memory time series with large fluctuations (heavy-tailed distributions). Two methods, which are the empirical characteristic function (ECF) procedure developed by Knight and Yu [The empirical characteristic function in time series estimation. Econometric Theory. 2002;18:691–721] and the Two-Step method (TSM) are proposed to estimate the parameters of stable ARFISMA model. The ECF method estimates simultaneously all the parameters, while the TSM considers in the first step the Markov Chains Monte Carlo–Whittle approach introduced by Ndongo et al. [Estimation of long-memory parameters for seasonal fractional ARIMA with stable innovations. Stat Methodol. 2010;7:141–151], combined with the maximum likelihood estimation method developed by Alvarez and Olivares [Méthodes d'estimation pour des lois stables avec des applications en finance. Journal de la Société Française de Statistique. 2005;1(4):23–54] in the second step. Monte Carlo simulations are also used to evaluate the finite sample performance of these estimation techniques.

Keywords:

• seasonal fractional ARIMA
• stable distributions
• ECF estimate
• whittle estimate
• Markov Chains Monte Carlo
• Two-Step method

Acknowledgments

Authors thank the Associate Editor and anonymous reviewers for their valuable comments and suggestions that helped improve the paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. The simulation results with other values of ψ are available to the authors upon request.

2. The boxplots of parameters for Model 3 and 4 are not shown here but are available to authors upon request.

Additional information

Funding

Mor Ndongo, Abdou Kâ Diongue and Aliou Diop acknowledge grants from CEA-MITIC, an African Center of Excellence in Mathematics, Informatics and ICT implemented by Gaston Berger University (Senegal).