A Simple R-estimation method for semiparametric duration models

Modeling nonnegative financial variables (e.g. durations between trades or volatilities) is central to a number of studies across econometrics, and still poses several statistical challenges. Among them, the efficiency aspects of semiparametric estimation remain pivotal. In this paper, we concentrate on estimation problems in autoregressive conditional duration models with unspecified innovation densities. Exponential quasi-likelihood estimators (QMLE) are the usual practice in that context, since they are easy-to-implement and preserve Fisher-consistency. However, the efficiency of the QMLE rapidly deteriorates away from the reference exponential density. To cope with the QMLE’s lack of accuracy, semiparametrically efficient procedures have been introduced. These procedures are obtained using the classical tangent space approach; they require kernel estimation and quite large sample sizes. We propose rank-based estimators (R-estimators) as a substitute. Just as the QMLE, R-estimators remain root-n consistent, irrespective of the underlying density, and rely on the choice of a reference density (which, however, needs not be the exponential one), under which they achieve semiparametric efficiency. Moreover, R-estimators neither require tangent space calculations nor kernel estimation. Numerical results illustrate that R-estimators based on the exponential reference density outperform the QMLE under a large class of actual innovation densities, such as the Weibull or Burr densities. A real-data example about modeling the price range of the Swiss stock market index concludes the paper.