Date of Award
1-1-2024
Document Type
Dissertation
Degree Name
Ph.D. in Mathematics
First Advisor
Martial Longla
Second Advisor
Martial Longla
Third Advisor
Xing Dang
Relational Format
dissertation/thesis
Abstract
This work explores the impact of perturbations of copulas on dependence and mixing properties for stationary ergodic Markov chains. We focus on two types of copula perturbations and establish their impact on the mixing properties of the Markov chains they generate. Examples are provided to illustrate the different perturbations explored. Furthermore, we delve into the analysis of a discrete Markov chain that is based on the Frechet family of copulas. The objective of this study is to explore the impact of discrete marginals on copula-based Markov chains. We analyze the mixing properties of such models to emphasize the difference between continuous and discrete state-space Markov chains. The Maximum likelihood approach is applied to derive estimators for model parameters in the case of a discrete state-space Markov chain with Bernoulli marginal distributions. A stationary case and a non-stationary case are considered. The asymptotic distributions of parameter estimators are provided. A simulation study showcases the performance of different estimators for the Bernoulli parameter of the marginal distribution. Some statistical tests are provided for model parameters.
Recommended Citation
Muia, Mathias Nthiani, "Dependence and Mixing for Perturbations of Copula-Based Markov Chains" (2024). Electronic Theses and Dissertations. 2847.
https://egrove.olemiss.edu/etd/2847