In a first part, we consider a doubly stochastic Poisson process with stochastic intensity function of a continuous semimartingale. An estimation procedure is proposed in a non parametrical setting for this function using a local polynomial estimator. We give a method to select the bandwidth in a non asymptotic framework, leading to an oracle inequality. A parametrical test is also proposed to test if the function belongs to some parametrical family.
In a second part, our results are used to model the dependence between electricity spot prices spikes and the wind penetration index in the European energy market. The wind penetration index is given by the ratio of the wind energy production divided by the total electricity production. We find that the wind penetration has an impact on the intensity of the spike occurrences in the electricity prices, and we formulate a joint model for electricity prices and wind penetration and calibrate it to recent data. We then use the new joint model in an application where we assess the impact of the modeling assumptions on the potential income of an electricity distributor who buys electricity from a wind farm operator.