On the (intradaily) seasonality and dynamics of a financial point process: a semiparametric approach

A new method of estimating a component model for the analysis of financial durations is proposed. The components are long-run dynamics and seasonality. The latter is left unspecified and the former is assumed to fall within the class of a certain family of parametric functions. The proposed estimation procedure is based on a generalized profile likelihood approach and requires the assumption either of a likelihood function for the model errors or, at least, that the error density belongs to the class of exponential densities. Its main interest is twofold: first, consistent and asymptotically normal estimators for both the parameters of the long-run stochastic component and the nonparametric curve that approximates the deterministic seasonal component are provided. Hence, it is possible to derive correct inference for both parametric and nonparametric components. Second, the method is computationally very appealing since 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 method is applied to price and volume durations of a stock traded at the NYSE, and compared to estimation with splines and with adjustment methods. It is shown that the proposed method outperforms the other methods.