Effective Measure of Endogeneity for the Autoregressive Conditional Duration Point Processes via Mapping to the Self-Excited Hawkes Process

TL;DR

This paper introduces a new measure of endogeneity for the ACD model by mapping it to the Hawkes process, enabling better understanding of internal versus external event influences.

Contribution

The paper proposes an endogeneity measure for the ACD model inspired by the Hawkes process, establishing a direct mapping to the Hawkes branching ratio.

Findings

The measure effectively quantifies internal feedback in the ACD model.

Numerical simulations validate the mapping between ACD endogeneity and Hawkes branching ratio.

The approach enhances understanding of endogenous versus exogenous event dynamics.

Abstract

In order to disentangle the internal dynamics from exogenous factors within the Autoregressive Conditional Duration (ACD) model, we present an effective measure of endogeneity. Inspired from the Hawkes model, this measure is defined as the average fraction of events that are triggered due to internal feedback mechanisms within the total population. We provide a direct comparison of the Hawkes and ACD models based on numerical simulations and show that our effective measure of endogeneity for the ACD can be mapped onto the "branching ratio" of the Hawkes model.