Title: Estimation for the Prediction of Point Processes with Many Covariates,
Abstract: Estimation of the intensity of a point process is considered within a
nonparametric framework. The intensity measure is unknown and depends on
covariates, possibly many more than the observed number of jumps. Only a single
trajectory of the counting process is observed. Interest lies in estimating the
intensity conditional on the covariates. The impact of the covariates is
modelled by an additive model where each component can be written as a linear
combination of possibly unknown functions. The focus is on prediction as
opposed to variable screening. Conditions are imposed on the coefficients of
this linear combination in order to control the estimation error. The rates of
convergence are optimal when the number of active covariates is large. As an
application, the intensity of the buy and sell trades of the New Zealand dollar
futures is estimated and a test for forecast evaluation is presented. A
simulation is included to provide some finite sample intuition on the model and
asymptotic properties.