An Alternative Semiparametric Regression Approach to Nonlinear Duration Modeling : Theory and Practice

This paper puts forward an alternative semiparametric regression approach to a nonlinear ACD modeling. The semiparametric functional form of the dependence of the conditional intensity on past durations suggests that the model be called the Semiparametric ACD (SEMI-ACD) model. The development of the SEMI-ACD model relies on two important factors; namely (i) an iterative estimation algorithm, which is devised to address the latency problem arises because the conditional expectation of duration with respect to the past history is not observable in practice, and (ii) an adaptive estimation of a partially linear additive autoregressive process. The theoretical study involves two fundamental issues. The first and by far the most important is the consistency of the estimation algorithm. Results will be exhibited for a variety of modes of consistency. Furthermore, to enrich the statistical rigor of the SEMI-ACD estimation procedure, the asymptotic properties of the semiparametric estimators are established under the conditions of the algorithm consistency. These asymptotic results are presented in conjunction with simulated examples which illustrate a robust finite-sample performance of the model. Finally, the paper applies the SEMI-ACD procedure to model the price duration process of the \$US/\$EUR exchange rate