On the (intradaily) Seasonality and Dynamics of a Financial Point Process: a Semiparametric Approach

A component model for the analysis of financial durations is proposed. The components are the long-run dynamics and the seasonality. The later is left unspecified and the former is assumed to fall within the class of certain family of parametric functions. The joint model is estimated by maximizing a (local) quasi-likelihood function, and the resulting nonparametric estimator of the seasonal curve has an explicit form that turns out to be a transformation of the Nadaraya-Watson estimator. The estimators of the parameters of interest are shown to be root-N consistent and asymptotically efficient. Furthermore, the seasonal curve is also estimated consistently. The methodology is applied to the trade duration process of Bankinter, a medium size Spanish bank traded in Bolsa de Madrid. We show that adjusting data by seasonality produces important misspecifications.