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

TL;DR

This paper introduces an estimation method based on the Empirical Characteristic Function for stable seasonal fractional ARIMA models, offering a robust alternative to maximum likelihood estimation, with proven consistency and normality.

Contribution

It develops and analyzes an ECF-based estimation approach for stable seasonal fractional ARIMA processes, demonstrating its theoretical properties and comparing it with existing MCMC Whittle methods.

Findings

ECF estimators are consistent and asymptotically normal.

The ECF method performs comparably or better than MCMC Whittle in simulations.

The approach overcomes robustness issues of traditional maximum likelihood methods.

Abstract

Maximum likelihood methods, while widely used, may be non-robust due to disagreement between the assumptions upon which the models are based and the true density probability distribution of observed data. Because the Empirical Characteristic Function (ECF) is the Fourier transform of the empirical distribution function, it retains all the information in the sample but can overcome difficulties arising from the likelihood. This paper discusses an estimation method via the ECF for stable seasonal fractional ARIMA processes. Under some assumptions, we show that the resulting estimators are consistent and asymptotically normally distributed. For comparison purpose, we consider also the MCMC Whittle method developed by Ndongo et al. (2010). The performance of the two methods is discussed using a Monte Carlo simulation.