Modeling non-stationarities in high-frequency financial time series

TL;DR

This paper investigates non-stationarities in high-frequency FTSE MIB index returns, proposes a non-homogeneous Poisson process model to describe them, and evaluates model selection criteria through simulations.

Contribution

It introduces a simple non-homogeneous Poisson process model for non-stationary high-frequency financial returns and assesses model selection methods via Monte Carlo simulations.

Findings

The proposed model can approximately reproduce stylized facts of high-frequency data.

Information criteria favor models with fewer parameters for compound Poisson models.

Model selection criteria perform poorly for the ACD model in some cases.

Abstract

We study tick-by-tick financial returns belonging to the FTSE MIB index of the Italian Stock Exchange (Borsa Italiana). We can confirm previously detected non-stationarities. However, scaling properties reported in the previous literature for other high-frequency financial data are only approximately valid. As a consequence of the empirical analyses, we propose a simple method for describing non-stationary returns, based on a non-homogeneous normal compound Poisson process. We test this model against the empirical findings and it turns out that the model can approximately reproduce several stylized facts of high-frequency financial time series. Moreover, using Monte Carlo simulations, we analyze order selection for this model class using three information criteria: Akaike's information criterion (AIC), the Bayesian information criterion (BIC) and the Hannan-Quinn information criterion (HQ). For comparison, we also perform a similar Monte Carlo experiment for the ACD (autoregressive conditional duration) model. Our results show that the information criteria work best for small parameter numbers for the compound Poisson type models, whereas for the ACD model the model selection procedure does not work well in certain cases.