Estimation of stable distribution parameters from a dependent sample

TL;DR

This paper introduces a new method for estimating stable distribution parameters from dependent samples using sample quantiles, demonstrating asymptotic normality and validating with simulations of stable moving average processes.

Contribution

It develops a quantile-based estimation approach tailored for dependent samples, extending stable distribution parameter estimation beyond independent data.

Findings

Estimates are asymptotically normal.

Asymptotic variance is derived for stable moving average processes.

Simulations confirm estimator effectiveness.

Abstract

Existing methods for the estimation of stable distribution parameters, such as those based on sample quantiles, sample characteristic functions or maximum likelihood generally assume an independent sample. Little attention has been paid to estimation from a dependent sample. In this paper, a method for the estimation of stable distribution parameters from a dependent sample is proposed based on the sample quantiles. The estimates are shown to be asymptotically normal. The asymptotic variance is calculated for stable moving average processes. Simulations from stable moving average processes are used to demonstrate these estimators.