ABSTRACT
Motivated from a project of analyzing call center data, time series models with infinitely divisible marginal distributions are studied. Existing models, though have a form similar to the classical ARMA model, have great restrictions. In this work we proposed two new constructions. The first one comes from the construction of multivariate random variables with infinitely divisible margins and gives more flexible moving average structure. The second one is based on the integration of Gamma random fields and gives continuous stationary stochastic processes with Gamma margins. Most of the properties about these new constructions carry over to the family of infinitely divisible distributions. Estimation procedures as well as their asymptotic properties are investigated. Open questions and future research directions are discussed.

This is a joint work with Dr. Lawrence Brown and Dr. Robert Wolpert.

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