  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.
