  Trawl processes belong to the class of continuous-time, strictly stationary,
infinitely divisible processes; they are defined as L\'{e}vy bases evaluated
over deterministic trawl sets. This article presents the first nonparametric
estimator of the trawl function characterising the trawl set and the serial
correlation of the process. Moreover, it establishes a detailed asymptotic
theory for the proposed estimator, including a law of large numbers and a
central limit theorem for various asymptotic relations between an in-fill and a
long-span asymptotic regime. In addition, it develops consistent estimators for
both the asymptotic bias and variance, which are subsequently used for
establishing feasible central limit theorems which can be applied to data. A
simulation study shows the good finite sample performance of the proposed
estimators and, in an empirical illustration, the new methodology is applied to
modelling and forecasting high-frequency financial spread data from a limit
order book.
