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Juan M. Rodríguez-Poo · David Veredas · Antoni Espasa<br />

Semiparametric estimation for f<strong>in</strong>ancial<br />

durations<br />

Abstract We propose a semiparametric model for the analysis <strong>of</strong> time series <strong>of</strong><br />

durations that show autocorrelation and determ<strong>in</strong>istic patterns. Estimation rests on<br />

generalized pr<strong>of</strong>ile likelihood, which allows for jo<strong>in</strong>t estimation <strong>of</strong> the parametric—<br />

an ACD type <strong>of</strong> model—and nonparametric components, provid<strong>in</strong>g consistent and<br />

asymptotically normal estimators. It is possible to derive the explicit form for the<br />

nonparametric estimator, simplify<strong>in</strong>g estimation to a standard maximum likelihood<br />

problem.<br />

Keywords Generalized pr<strong>of</strong>ile likelihood · ACD model · Seasonality<br />

JEL Classification C14 · C15 · C22 · C32<br />

1 Introduction<br />

Model<strong>in</strong>g f<strong>in</strong>ancial durations has been a very active area <strong>of</strong> research s<strong>in</strong>ce Engle and<br />

Russell (1998) <strong>in</strong>troduced the autoregressive conditional duration (ACD) model.<br />

Their analysis is justified from an economic and a statistical po<strong>in</strong>t <strong>of</strong> view. Market<br />

microstructure theory shows that the time between events <strong>in</strong> stock markets conveys<br />

<strong>in</strong>formation that is used by market participants. On the other hand, f<strong>in</strong>ancial durations<br />

are one-dimensional po<strong>in</strong>t processes (with time as space) and the analysis <strong>of</strong><br />

these processes has a long tradition <strong>in</strong> statistics.<br />

S<strong>in</strong>ce the ACD model, a plethora <strong>of</strong> modifications and alternatives have been<br />

proposed. Bauwens and Giot (2000) <strong>in</strong>troduce the Log-ACD model, an exponential<br />

Juan M. Rodríguez-Poo<br />

Departamento de Economía, niversidad de Cantabria, E-39005 Santander, Belgium<br />

David Veredas<br />

Universite Libre de Bruxelles (ECARES), 50 Ave Jeanne CP114 B1050 Brussels, Belgium<br />

David Veredas<br />

CORE, Université Catholique de Louva<strong>in</strong>, Louva<strong>in</strong>, Belgium<br />

Antoni Espasa<br />

Departamento de Estadística y Econometría, Universidad Carlos III de Madrid, E-28903 Getafe,<br />

Spa<strong>in</strong>

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