Integer-Valued Trawl Processes: A Class of Stationary Infinitely Divisible Processes

Abstract

This paper introduces a new continuous-time framework for modelling serially correlated count and integer-valued data. The key component in our new model is the class of integer-valued trawl (IVT) processes, which are serially correlated, stationary, infinitely divisible processes. We analyse the probabilistic properties of such processes in detail and, in addition, study volatility modulation and multivariate extensions within the new modelling framework. Moreover, we illustrate in a simulation study how our new models can be estimated.

Keywords: Lévy bases, trawl processes, stationarity, stochastic volatility, meta-time change

JEL Classification: C22, C51, C60