Copula-based markov chain logistic regression modeling on binomial time series data

Abstract

A first-order autoregressive time series model with binomial distributed random variables has been developed using the copula-based Markov chain model approach. By still utilizing conditional probability, covariate variables can also be included in the model and can be assumed as the independent variable. The time series dependent variable with a binomial distribution and continuous independent variables can be modelled using a copula-based Markov chain model with the probability of success expressed in the logit model. This study proposes a copula-based Markov chain logistic regression model with marginal binomial and joint distribution functions built through the copula function. Besides that, this study aims to estimate the parameters involved in the model. The parameters are the parameters of the logistic regression model as the relationship between the dependent and independent variables and the copula parameter as a time dependency. Using the bivariate copula functions are Clayton, Gumbel and Frank, the parameter estimation method is Maximum Likelihood Estimation (MLE). Simulations were carried out to see the efficiency of the parameter estimation and asymptotic results. Based on the simulation results, it was concluded that MLE provides an accurate estimate of the copula-based Markov chain logistic regression. In addition, the copula-based Markov chain logistic regression model can not only see the relationship between the independent and dependent variables but also provide an estimate of the time dependency of the dependent variable. The following are some of the proposed approach's highlights:•This method proposes a binomial time series data model with covariate variables by combining the logistic regression model and the first-order Markov chain model.•Parameter estimation in this model uses the Maximum Likelihood Estimation method.•The model provides the possibility to see the relationship between variables and the time dependency.