Model diagnostic procedures for copula-based Markov chain models for statistical process control

Investigating serial dependence is an important step in statistical process control (SPC). One recent approach is to fit a copula-based Markov chain model to perform SPC, which provides an attractive alternative to the traditional AR1 model. However, methodologies for model diagnostic have not been considered. In this paper, we develop two different approaches for model diagnostic procedures for copula-based Markov chain models. The first approach employs a formal test based on the Kolmogorov-Smirnov or the Cramér-von Mises statistics with aid of a parametric bootstrap. The second approach employs the second-order Markov chain model to examine the Markov property in the model. This second approach itself is a new SPC method. We made all the computing methodologies available in the R Copula.Markov package, and check their performance by simulations. We analyze three datasets for illustration.