AbstractsMathematics

Estimation with stable disturbances

by Novin Ghaffari




Institution: University of Texas – Austin
Department: Statistics
Degree: MSin Statistics
Year: 2015
Keywords: Stable distributions; Characteristic function; Lévy process; ARMA model
Record ID: 2059234
Full text PDF: http://hdl.handle.net/2152/29165


Abstract

The family of stable distributions represents an important generalization of the Gaussian family; stable random variables obey a generalized central limit theorem where the assumption of finite variance is replaced with one of power law decay in the tails. Possessing heavy tails, asymmetry, and infinite variance, non-Gaussian stable distributions can be suitable for inference in settings featuring impulsive, possibly skewed noise. A general lack of analytical form for the densities and distributions of stable laws has prompted research into computational methods of estimation. This report introduces stable distributions through a discussion of their basic properties and definitions in chapter 1. Chapter 2 surveys applications, and chapter 3 discusses a number of procedures for inference, with particular attention to time series models in the ARMA setting. Further details and an application can be found in the appendices.