# Performance of information criteria used for model selection of Hawkes process models of financial data

## TL;DR

This study evaluates the effectiveness of AIC, BIC, and HQ information criteria in selecting the correct order of Hawkes process models for high-frequency financial data, considering sample size effects.

## Contribution

It provides a systematic comparison of IC performance in model selection for Hawkes processes using simulated data with realistic parameters.

## Key findings

- BIC outperforms AIC and HQ in correct model selection.
- Sample size significantly influences IC accuracy.
- Results align with theoretical predictions and empirical data.

## Abstract

We test three common information criteria (IC) for selecting the order of a Hawkes process with an intensity kernel that can be expressed as a mixture of exponential terms. These processes find application in high-frequency financial data modelling. The information criteria are Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn criterion (HQ). Since we work with simulated data, we are able to measure the performance of model selection by the success rate of the IC in selecting the model that was used to generate the data. In particular, we are interested in the relation between correct model selection and underlying sample size. The analysis includes realistic sample sizes and parameter sets from recent literature where parameters were estimated using empirical financial intra-day data. We compare our results to theoretical predictions and similar empirical findings on the asymptotic distribution of model selection for consistent and inconsistent IC.