A Point on Discrete versus Continuous State-Space Markov Chains

TL;DR

This paper investigates how discrete marginal distributions influence copula-based Markov chains, focusing on mixing properties, parameter estimation, and differences from continuous state-space models, supported by simulations and statistical tests.

Contribution

It introduces estimators for model parameters in discrete copula-based Markov chains and compares their performance with continuous models, highlighting key differences.

Findings

Maximum likelihood estimators for $p$ are asymptotically normal.

Simulation results compare estimator performances.

Statistical tests for model parameters are developed.

Abstract

This paper examines the impact of discrete marginal distributions on copula-based Markov chains. We present results on mixing and parameter estimation for a copula-based Markov chain model with Bernoulli($p$) marginal distribution and highlight the differences between continuous and discrete state-space Markov chains. We derive estimators for model parameters using the maximum likelihood approach and discuss other estimators of $p$ that are asymptotically equivalent to its maximum likelihood estimator. The asymptotic distributions of the parameter estimators are provided. A simulation study showcases the performance of the different estimators of $p$. Additionally, statistical tests for model parameters are included.