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A Simple R-Estimation Method for Semiparametric Duration Models

Marc Hallin () and Davide La Vecchia

No ECARES 2017-01, Working Papers ECARES from ULB -- Universite Libre de Bruxelles

Abstract: Modeling nonnegative financial variables (e.g. durations between trades, traded volumes or asset volatilities) is central to a number of studies across financial econometrics, and, despite the efforts, still poses several statistical challenges. Among them, the efficiency aspects of semiparametric estimation. In this paper, we concentrate on estimation problems in Autoregressive Conditional Duration (ACD) models with unspecified innovation densities. Exponential quasi-likelihood estimators (QMLE) are the usual practice in that context. The efficiency of those QMLEs (the only Fisher-consistent QMLEs) unfortunately rapidly deteriorates away from the reference exponential density—a phenomenon that has been emphasized earlier by Drost and Werker (2003), who propose various semiparametrically efficient procedures to palliate that phenomenon. Those procedures rely on a general semiparametric approach which typically requires kernel estimation of the underlying innovation density. 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 under which they achieve semiparametric efficiency; that density, however, needs not be the exponential one. Contrary to the semiparametric estimators proposed by Drost and Werker (2003), R-estimators neither require tangent space calculations nor kernel-based density estimation. Numerical results moreover indicate that R-estimators based on exponential reference densities uniformly outperform the exponential QMLE under such families of innovations as the Weibull or Burr densities. A real data example about modeling the price range of the Swiss stock market index concludes the paper.

Keywords: efficiency; irregularly spaced data; quasi-likelihood; ranks; local asymptotic normality (search for similar items in EconPapers)
JEL-codes: C01 C14 C41 C50 (search for similar items in EconPapers)
New Economics Papers: this item is included in nep-ecm
Date: 2017-01
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