Comparative Study of Estimation Methods for a New Family of Copula-Based Reversible Markov Chains

This work explores continuous state–space stationary reversible Markov chains generated by a new family of absolutely continuous symmetric copulas that have piecewise constant densities. We compare three parameter estimation techniques for the Markov chains generated by these copulas. Furthermore, we provide the Central Limit Theorems, χ2-tests and confidence intervals based on these estimators. A simulation study performed using R 4.4.1 is described to support the findings.