A point on discrete versus continuous state-space Markov chains

Abstract This article investigates the effects of discrete marginal distributions on copula-based Markov chains. We establish results on mixing properties and parameter estimation for a copula-based Markov chain model with Bernoulli( <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p ) marginal distributions, emphasizing some distinctions between continuous and discrete state-space Markov chains. We derive parameter estimators using the maximum-likelihood estimation (MLE) method and explore alternative estimators of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p that are asymptotically equivalent to the MLE. Furthermore, we provide the asymptotic distributions of these parameter estimators. A simulation study is conducted to evaluate the performance of the various estimators for <m:math xmlns:m="http://www.w3.org/1998/Math/MathML"> <m:mi>p</m:mi> </m:math> p . Additionally, we employ the likelihood ratio test to assess independence within the sequence.