Jackknife Empirical Likelihood Ratio Test for Cauchy Distribution

TL;DR

This paper introduces a new goodness-of-fit test for the Cauchy distribution using jackknife empirical likelihood methods, evaluated through simulations and real data applications, to better model heavy-tailed data.

Contribution

It develops a novel jackknife empirical likelihood ratio test specifically for the Cauchy distribution, enhancing goodness-of-fit testing in heavy-tailed data scenarios.

Findings

The test performs well in finite samples based on simulation results.

The method effectively analyzes real-world heavy-tailed data sets.

Abstract

Heavy-tailed distributions, such as the Cauchy distribution, are acknowledged for providing more accurate models for financial returns, as the normal distribution is deemed insufficient for capturing the significant fluctuations observed in real-world assets. Data sets characterized by outlier sensitivity are critically important in diverse areas, including finance, economics, telecommunications, and signal processing. This article addresses a goodness-of-fit test for the Cauchy distribution. The proposed test utilizes empirical likelihood methods, including the jackknife empirical likelihood (JEL) and adjusted jackknife empirical likelihood (AJEL). Extensive Monte Carlo simulation studies are conducted to evaluate the finite sample performance of the proposed test. The application of the proposed test is illustrated through the analysing two real data sets.