Shephard, NeilYang, Justin2018-01-172015Shephard, Neil, and Justin J. Yang. 2016. "Likelihood inference for exponential-trawl processes." In The Fascination of Probability, Statistics and their Applications, eds. Podolskij, M., Stelzer, R., Thorbjørnsen, S., Veraart, A.E.D.: 251-281.Cham, Switzerland: Springer International.978-3-319-25826-3http://nrs.harvard.edu/urn-3:HUL.InstRepos:34650467Integer-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.en-USMonograph or Book2018-01-1710.1007/978-3-319-25826-3_12