A copula-based bivariate integer-valued autoregressive process with application

TL;DR

This paper introduces a bivariate integer-valued autoregressive model using copulas to capture dependence, compares estimation methods through simulations, and applies the model to loan default data with various copula and distribution choices.

Contribution

It develops a new copula-based BINAR(1) model, analyzes estimation techniques, and demonstrates its application to real-world loan default data.

Findings

Copula dependence parameter estimation varies with methods.

Model effectively captures dependence in loan default data.

Different copula and marginal distribution combinations impact model fit.

Abstract

A bivariate integer-valued autoregressive process of order 1 (BINAR(1)) with copula-joint innovations is studied. Different parameter estimation methods are analyzed and compared via Monte Carlo simulations with emphasis on estimation of the copula dependence parameter. An empirical application on defaulted and non-defaulted loan data is carried out using different combinations of copula functions and marginal distribution functions covering the cases where both marginal distributions are from the same family, as well as the case where they are from different distribution families.