Parametric quantile autoregressive conditional duration models with application to intraday value-at-risk

TL;DR

This paper introduces a new quantile-based extension of autoregressive conditional duration models for high-frequency financial data, enabling the modeling of different percentiles and improving intraday value-at-risk estimation.

Contribution

It proposes a novel quantile log-symmetric ACD model, extending traditional models to capture various percentiles and providing a comprehensive theoretical and empirical analysis.

Findings

The model accurately estimates different duration percentiles.

Simulation studies confirm reliable parameter recovery.

Application to financial data improves intraday VaR estimation.

Abstract

The modeling of high-frequency data that qualify financial asset transactions has been an area of relevant interest among statisticians and econometricians -- above all, the analysis of time series of financial durations. Autoregressive conditional duration (ACD) models have been the main tool for modeling financial transaction data, where duration is usually defined as the time interval between two successive events. These models are usually specified in terms of a time-varying mean (or median) conditional duration. In this paper, a new extension of ACD models is proposed which is built on the basis of log-symmetric distributions reparametrized by their quantile. The proposed quantile log-symmetric conditional duration autoregressive model allows us to model different percentiles instead of the traditionally used conditional mean (or median) duration. We carry out an in-depth study of theoretical properties and practical issues, such as parameter estimation using maximum likelihood method and diagnostic analysis based on residuals. A detailed Monte Carlo simulation study is also carried out to evaluate the performance of the proposed models and estimation method in retrieving the true parameter values as well as to evaluate a form of residuals. Finally, the proposed class of models is applied to a price duration data set and then used to derive a semi-parametric intraday value-at-risk (IVaR) model.