# Semiparametric Autoregressive Conditional Duration Model: Theory and Practice

50 Pages Posted: 5 Sep 2012 Last revised: 6 Sep 2012

See all articles by Patrick Saart

## Patrick Saart

University of Canterbury

## Jiti Gao

Monash University - Department of Econometrics & Business Statistics

## David E. Allen

School of Mathematics and Statistics, The University of Sydney; Financial Research Network (FIRN); Department of Finance; School of Business and Law, Edith Cowan University

Date Written: July 25, 2012

### Abstract

Many existing extensions of the Engle and Russell's (1998) Autoregressive Conditional Duration (ACD) model in the literature are aimed at providing additional exibility either on the dynamics of the conditional duration model or the allowed shape of the hazard function, i.e. its two most essential components. This paper introduces an alternative semiparametric regression approach to a nonlinear ACD model; the use of a semiparametric functional form on the dynamics of the duration process suggests the model being called the Semiparametric ACD (SEMI{ACD) model. Unlike existing alternatives, the SEMI{ACD model allows simultaneous generalizations on both of the above{mentioned components of the ACD framework. To estimate the model, we establish an alternative use of the existing Buhlmann and McNeil's (2002) iterative estimation algorithm in the semiparametric setting and provide the mathematical proof of its statistical consistency in our context. Furthermore, we investigate the asymptotic properties of the semiparametric estimators employed in order to ensure the statistical rigor of the SEMI{ACD estimation procedure. These asymptotic results are presented in conjunction with simulated examples, which provide an empirical evidence of the SEMI{ACD model's robust nite{sample performance. Finally, we apply the proposed model to study price duration process in the foreign exchange market to illustrate its usefulness in practice.

Keywords: Dependent point process, duration, hazard rate and random measure, irregularly

JEL Classification: C14, C41, F31

Suggested Citation

Saart, Patrick and Gao, Jiti and Allen, David Edmund, Semiparametric Autoregressive Conditional Duration Model: Theory and Practice (July 25, 2012). Available at SSRN: https://ssrn.com/abstract=2141546 or http://dx.doi.org/10.2139/ssrn.2141546

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