Parametric Quantile Autoregressive Conditional Duration Models With Application to Intraday Value‐at‐Risk Forecasting

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, we derive a semiparametric intraday value‐at‐risk (IVaR) model and then the proposed models are applied to two price duration data sets.