GenMarkov: Modeling Generalized Multivariate Markov Chains in R

TL;DR

This paper introduces GenMarkov, a generalized multivariate Markov chain model in R that incorporates exogenous variables and non-homogeneity, with demonstrated effectiveness through simulations and real data application.

Contribution

The work presents a novel Markov chain model that accounts for exogenous variables and non-homogeneity, along with an R package implementation.

Findings

Model effectively detects non-homogeneous Markov chains

Empirical application estimates transition probabilities with exogenous variables

Simulation confirms model's robustness in various scenarios

Abstract

This article proposes a new generalization of the Multivariate Markov Chains (MMC) model. The future values of a Markov chain commonly depend on only the past values of the chain in an autoregressive fashion. The generalization proposed in this work also considers exogenous variables that can be deterministic or stochastic. Furthermore, the effects of the MMC's past values and the effects of pre--determined or exogenous covariates are considered in our model by considering a non--homogeneous Markov chain. The Monte Carlo simulation study findings showed that our model consistently detected a non--homogeneous Markov chain. Besides, an empirical illustration demonstrated the relevance of this new model by estimating probability transition matrices over the space state of the exogenous variable. An additional and practical contribution of this work is the development of a novel R package with this generalization.