Computational methods for a copula-based Markov chain model with a binomial time series

Abstract

A copula-based Markov chain model can flexibly capture serial dependence in a time series. However, the computational developments for copula-based Markov models remain insufficient for discrete marginal models compared with continuous ones. In this article, we develop computational methods for a binomial time series under the Clayton and Joe copulas. The methods include the data-generation, parameter estimation, model selection, and goodness-of-fit tests. We implement the methods in our R package Copula.Markov (https://CRAN.R-project.org/package=Copula.Markov). We conduct simulations to see the performance of the developed methods. Finally, the proposed method is illustrated by a real dataset.

Keywords:

• Binomial distribution
• Clayton copula
• Discrete-valued time series
• Goodness-of-fit
• Maximum likelihood estimation
• Serial dependence

MATHEMATICS SUBJECT CLASSIFICATION:

• 62M10
• 62H12
• 62H20
• 60J20

Acknowledgment

We thank reviewers for their helpful comments that improved the manuscript. We thank Mr. Weiru Chen for his prior contribution through his Master thesis.

Conflict of interest

On behalf of all authors, the corresponding author states that there is no conflict of interest.

Additional information

Funding

Emura T is financially supported by MOST:107-2118-M-008-003-MY3 from Ministry of Science and Technology, Taiwan.