Likelihood inference for exponential-trawl processes

TL;DR

This paper develops likelihood inference methods for exponential-trawl processes, a class of stationary, infinitely divisible processes, using prediction, filtering, smoothing, and EM algorithms, enabling scalable analysis of these complex models.

Contribution

It provides the first likelihood inference framework for exponential-trawl processes, integrating prediction, filtering, smoothing, and EM algorithms for these models.

Findings

First likelihood inference method for exponential-trawl processes.

Development of scalable EM algorithm for parameter estimation.

Framework adaptable to more general trawl processes.

Abstract

Integer-valued trawl processes are a class of serially correlated, stationary and infinitely divisible processes that Ole E. Barndorff-Nielsen has been working on in recent years. In this Chapter, we provide the first analysis of likelihood inference for trawl processes by focusing on the so-called exponential-trawl process, which is also a continuous time hidden Markov process with countable state space. The core ideas include prediction decomposition, filtering and smoothing, complete-data analysis and EM algorithm. These can be easily scaled up to adapt to more general trawl processes but with increasing computation efforts.