Multivariate Pareto Minification Processes

Abstract

Autoregressive (AR) and autoregressive moving average (ARMA) processes with multivariate exponential (ME) distribution are presented and discussed. The theory of positive dependence is used to show that in many cases, multivariate exponential autoregressive (MEAR) and multivariate autoregressive moving average (MEARMA) models consist of associated random variables. Also, we present special cases of the multivariate exponential autoregressive process in which the multivariate process is stationary and has well-known multivariate exponential distribution.

Keywords: Marshall-Olkin multivariate Pareto distribution; Autoregressive minification processes of order 1 and k; Stationary marginal distribution; Joint survival function; Characterizations.