Develop a dependent marked version where mark sizes influence intensities

Develop and analyze a dependent marked version of the proposed multivariate self- and mutually exciting point process with flexible residuals, in which the mark size of each event affects the subsequent λ processes, rather than assuming independent marks.

Background

In the empirical applications, the paper treats the mark sizes (price jump magnitudes) as independent and not influencing future intensities to keep the model tractable. This simplifies estimation and simulation but omits potentially important dependence between mark sizes and subsequent event intensities.

The authors explicitly state that allowing marks to affect the intensity is feasible but increases complexity, and they leave this dependent marked extension for future research.