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.Comment: 29 pages, 6 figures, forthcoming in: "A Fascinating Journey through
Probability, Statistics and Applications: In Honour of Ole E.
Barndorff-Nielsen's 80th Birthday", Springer, New Yor
