  In this paper, we focus on a new generalization of multivariate general
compound Hawkes process (MGCHP), which we referred to as the multivariate
general compound point process (MGCPP). Namely, we applied a multivariate point
process to model the order flow instead of the Hawkes process. Law of large
numbers (LLN) and two functional central limit theorems (FCLTs) for the MGCPP
were proved in this work. Applications of the MGCPP in the limit order market
were also considered. We provided numerical simulations and comparisons for the
MGCPP and MGCHP by applying Google, Apple, Microsoft, Amazon, and Intel trading
data.
