Semiparametric autoregressive conditional duration model: Theory and practice

Many existing extensions of the Engle and Russell's (1998 Engle , R. , Russell , J. , 1998 . Autoregressive conditional duration: A new model for irregularly spaced transaction data . Econometrica 66 : 1127 – 1162 . [Crossref], [Web of Science ®], , [Google Scholar] ) Autoregressive Conditional Duration (ACD) model in the literature are aimed at providing additional flexibility 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 article 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 Bühlmann and McNeil's (2002 Bühlmann , P. , McNeil , A. ( 2002 ). An algorithm for nonparametric GARCH modelling . Computational Statistics & Data Analysis 40 : 665 – 683 . [Crossref], [Web of Science ®], , [Google Scholar] ) 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 finite-sample performance. Finally, we apply the proposed model to study price duration process in the foreign exchange market to illustrate its usefulness in practice