SOME MULTIVARIATE DISCRETE TIME SERIES MODELS FOR DEPENDENT MULTIVARIATE ZIPF COUNTS

A family of models MD-AR(1), MD-AR(p), MD-MA(q), MD-ARMA(p, q) for multivariate discrete time series is developed and all their autocorrelation structures are investigated. Any fat-tailed dependent multivariate discrete random vectors can be fitted reasonably by these multivariate discrete time series models. In this article, four multivariate Zipf processes are mainly discussed. Some distributional properties of the Zipf processes, MZ-AR(1) and MZ-MA(1) including the joint distribution, time reversibility, expected run length, extreme order statistics, geometric minima are studied thoroughly in this paper. These multivariate Zipf processes provide potential models for multivariate discrete income time series data.