The UHF-GARCH-Type Model in the Analysis of Intraday Volatility and Price Durations – the Bayesian Approach

Abstract

In empirical research on financial market microstructure and in testing some
predictions from the market microstructure literature, the behavior of some
characteristics of trading process can be very important and useful. Among
all characteristics associated with tick-by-tick data, the trading time and the
price seem the most important. The very first joint model for prices and
durations, the so-called UHF-GARCH, has been introduced by Engle (2000).
The main aim of this paper is to propose a simple, novel extension of Engle’s
specification based on trade-to-trade data and to develop and apply the Bayesian
approach to estimation of this model. The intraday dynamics of the return
volatility is modelled by an EGARCH-type specification adapted to irregularly
time-spaced data. In the analysis of price durations, the Box-Cox ACD model
with the generalized gamma distribution for the error term is considered. To
the best of our knowledge, the UHF-GARCH model with such a combination
of the EGARCH and the Box-Cox ACD structures has not been studied
in the literature so far. To estimate the model, the Bayesian approach is
adopted. Finally, the methodology developed in the paper is employed to
analyze transaction data from the Polish Stock Market.