An algorithm for the computation of joint Hawkes moments with exponential kernel
This provides a tool for researchers in stochastic processes and finance to compute complex statistical measures more efficiently, though it is incremental as it builds on existing Hawkes process theory.
The paper tackles the computational challenge of deriving closed-form expressions for joint moments and cumulants of Hawkes processes with exponential kernels, presenting a recursive algorithm implemented in Maple and Mathematica that handles expansions of up to 27,116 summands for fifth moments.
The purpose of this paper is to present a recursive algorithm and its implementation in Maple and Mathematica for the computation of joint moments and cumulants of Hawkes processes with exponential kernels. Numerical results and computation times are also discussed. Obtaining closed form expressions can be computationally intensive, as joint fifth cumulant and moment formulas can be respectively expanded into up to 3,288 and 27,116 summands.