Semiparametric Autoregressive Conditional Duration Model: Theory and Practice

Abstract

Many existing extensions of the Engle and Russell\u27s (1998) 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\u27s (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\u27s 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

Econometric Time Series Specification Testing in a Class of Multiplicative Error Models

“…Furthermore, the simplest form of the semiparametric ACD model proposed by Saart et al (2013), i.e. the so-called SEMI-ACD(1,1) model, defines…”

“…where ν t denotes the observed price duration as constructed in the previous paragraph and φ(i t−1 ) denotes an intraday diurnal factor. Following Saart et al (2013), we estimate the diurnal factor φ(i t−1 ) of the calendar time i t−1 at which the tth duration begins using the kernel regression smoothing technique with the smoother defined as…”

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

“…Further, Saart et al . () establish the consistency as well as asymptotic normality of the kernel‐based estimator of the parametric component of SEMI‐ACD model. An empirical evidence in support of the robust finite sample performance of the SEMI‐ACD model is provided by applying it to study the price duration process in the foreign exchange market published over the Reuters' network, specifically, the US dollar to Euro exchange rate data.…”

“…Saart et al . () classify the ACD models into three generations. The entire first generation of the ACD models has been developed with the assumption that the innovations follow a distribution with nonnegative support.…”

“…Saart et al . () propose to use an alternative semiparametric approach to the above‐mentioned parametric and nonparametric models. This approach takes into account the existing information about linearity.…”