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

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An extended generalised partially linear single-index (EGPLSI) model provides flexibility of a partially linear model and a single-index model. Furthermore, it also allows for the analysis of the shape-invariant specification. Nonetheless, the model's practicality in the empirical studies has been hampered by lack of appropriate estimation procedure and method to deal with endogeneity. In the current paper, we establish an alternative control function approach to address the endogeneity issue in the estimation of the EGPLSI model. We also show that all attractive features of the EGPLSI model discussed in the literature are still available under the proposed estimation procedure. Economic literature suggests that semiparametric technique is an important tool for an empirical analysis of Engel curves, which often involves endogeneity of the total expenditure. We show that our newly developed method is applicable and able to address the endogeneity issue involved in semiparametric analysis of the empirical Engel curves.