ctmcd: An R Package for Estimating the Parameters of a Continuous-Time Markov Chain from Discrete-Time Data

This article introduces the R package ctmcd, which provides an implementation of methods for the estimation of the parameters of a continuous-time Markov chain given that data are only available on a discrete-time basis. This data consists of partial observations of the state of the chain, which are made without error at discrete times, an issue also known as the embedding problem for Markov chains. The functions provided comprise matrix logarithm based approximations as described in Israel et al. (2001), as well as Kreinin and Sidelnikova (2001), an expectation-maximization algorithm and a Gibbs sampling approach, both introduced by Bladt and Sørensen (2005). For the expectationmaximization algorithm Wald confidence intervals based on the Fisher information estimation method of Oakes (1999) are provided. For the Gibbs sampling approach, equal-tailed credibility intervals can be obtained. In order to visualize the parameter estimates, a matrix plot function is provided. The methods described are illustrated by Standard and Poor’s discrete-time corporate credit rating transition data.