Copula-based Markov Chain Models for Stationary Time Series—Parametric Estimation and Statistical Process Control—

Abstract

This article introduces copula-based Markov chain models to be fitted for a serially correlated time series. As their major applications, we also review statistical process control methods under the normal distribution model. We first give a general introduction to copulas and Markov chain models to explain the mathematical properties of copulas for modeling correlated data. Next, we introduce copula-based Markov chain models and various statistical inference procedures, such as the maximum likelihood estimation under the normal distribution model. We provide several real data examples to demonstrate the usefulness of the proposed methods. Appendix contains our R codes for reproducing the data analysis results.