Parameter estimation in models generated by SDE's with symmetric alpha stable noise

TL;DR

This paper introduces an improved one-step estimator for models driven by Levy processes with symmetric alpha-stable noise, along with numerical optimization methods and software for testing and comparison.

Contribution

It presents a novel improved estimator for Levy process models and provides combined numerical methods and software for effective estimation and comparison.

Findings

The improved estimator enhances accuracy in Levy process models.

Numerical methods facilitate efficient optimization.

Software implementation enables practical testing and comparison.

Abstract

The article considers vector parameter estimators in statistical models generated by Levy processes. An improved one step estimator is presented that can be used for improving any other estimator. Combined numerical methods for optimization problems are proposed. A software has been developed and a correspondent testing and comparison have been presented.