Simulation methods and error analysis for trawl processes and ambit fields

TL;DR

This paper introduces new simulation algorithms for trawl processes and ambit fields, analyzing their error bounds, convergence, and computational complexity, with practical recommendations for implementation.

Contribution

It presents novel simulation algorithms for trawl processes and ambit fields, including error analysis and methods to reduce computational costs.

Findings

New algorithms for simulating trawl processes with error bounds.

Extension of simulation methods to ambit fields.

Analysis of computational complexity and implementation strategies.

Abstract

Trawl processes are continuous-time, stationary and infinitely divisible processes which can describe a wide range of possible serial correlation patterns in data. In this paper, we introduce new simulation algorithms for trawl processes with monotonic trawl functions and establish their error bounds and convergence properties. We extensively analyse the computational complexity and practical implementation of these algorithms and discuss which one to use depending on the type of L\'evy basis. We extend the above methodology to the simulation of kernel-weighted, volatility modulated trawl processes and develop a new simulation algorithm for ambit fields. Finally, we discuss how simulation schemes previously described in the literature can be combined with our methods for decreased computational cost.