Modeling marked point processes using bivariate mixture transition distribution models

We propose new statistical models for the analysis of marked point processes. These models deal with data that arrives in unequal intervals, such as financial transactions or heart attacks. The models treat both the time between event arrivals and the observed marks as stochastic processes. We propose and investigate a class of bivariate distributions to form the bivariate mixture transition distribution (BMTD). In these models the bivariate conditional distribution of the next observation given the past is a mixture of conditional distributions given each one of the last k observations. The identifiability of the model is investigated, and the EM algorithm is developed to obtain estimates of the model parameters