Conditional Duration Models for High‐frequency Data: A Review on Recent Developments

Abstract

This paper reviews the recent literature on conditional duration modeling in high‐frequency finance. These conditional duration models are associated with the time interval between trades, price, and volume changes of stocks, traded in a financial market. An earlier review by Pacurar provides an exhaustive survey of the first and some of the second generation conditional duration models. We consider almost all of the third‐generation and some of the second‐generation conditional duration models. Notable applications of these models and related empirical studies are discussed. The paper may be seen as an extension to Pacurar.

Jointly Modeling Autoregressive Conditional Mean and Variance of Non-Negative Valued Time Series

“…is a restriction imposed not just by the baseline model but many of the multiplicative model specifications considered in the extensive literature on non-negative time series models as reviewed in Bhogal and Variyam (2019); Pacurar (2008). This proportionality restriction may not adequately capture the conditional dynamics of time series leading to, for example, the well known problem of over-or under-dispersion.…”

“…The multiplicative error model belongs to the class of observation driven models where the dynamics is driven by the lagged values of the observed data (Cox 1981). Although several variations of the multiplicative error model have been proposed (Bhogal and Variyam 2019;Brownlees et al 2012;Pacurar 2008), the literature to date has focused mostly on modeling the dynamics of the conditional mean (first moment) process as an autoregression.…”

A micro‐to‐macro approach to returns, volumes and waiting times

“…The cornerstone of this approach is to consider the observed price to be a collateral effect of an unobservable volatility process to which a noise process transformation is applied, see, for example Reference 1. This line of research has flourished during the last two decades and considerable attention has been dedicated to the problem of irregular spacing in time of observations when dealing with high frequency financial data; the seminal work by Engle 2 and the recent review by Bhogal and Thekke Variyam 3 can provide a wide overview of the subject. Rapidly, econometricians turned the attention on multivariate models of logarithmic price returns, volumes and duration (waiting times), the latter to be intended as the time interval between changes in trades, price and volume of stocks, see for example References 4‐7…”

A General Family of Autoregressive Conditional Duration Models Applied to High-Frequency Financial Data

“…The usefulness of appropriately modeling duration data is stressed by the relatively recent market microstructure literature; see Diamond and Verrechia (1987), Easley and O'Hara (1992), and Easley et al (1997). Generalizations of the original ACD model are basically based on the following three aspects, i.e., (a) the distributional assumption in order to yield a unimodal failure rate (FR) (Grammig and Maurer 2000;Lunde 1999), (b) the linear form for the conditional mean (median) dynamics (Allen et al 2008;Bauwens and Giot 2000;Fernandes and Grammig 2006), and (c) the time series properties (Bauwens and Giot 2003;Chiang 2007;De Luca and Zuccolotto 2006;Jasiak 1998;Zhang et al 2001); see the reviews by Pacurar (2008) and Bhogal and Variyam Thekke (2019). Bhatti (2010) proposed a generalization of the ACD model that falls into all three branches above, based on the Birnbaum-Saunders (BS) distribution, denoted as the BS-ACD model.…”