A New Time Series Model for Transaction Data and Marked Point Processes

Abstract

We propose a new time series model for the bivariate/multivariate transaction data, where model their joint transition dynamics by directly modeling the conditional distribution of the current observation to be a mixture of conditional distributions given the past p-lags information. Each joint multivariate conditional distribution in the mixture is constructed via a certain class of Copula. Such model can successfully capture some distinguished nonlinear non-Gaussian time series features, such as the irregular bursts or jumps that are so widely observed in the transaction data set and other more general marked point processes. We illustrate the new time series model and related methods by modeling three pieces of IBM stock transaction data, and show its advantages over some benchmark models.