B0508
Title: yuima.PPR: New developments for the point process in the YUIMA package.
Authors: Lorenzo Mercuri - University of Milan (Italy) [presenting]
Abstract: The purpose is to present and discuss yuima classes and methods that allow the user to simulate and estimate a Point Process Regression Model (PPR). The PPR model can be seen as a generalization of a self-exciting point process, since it is possible to consider external covariates that explain the behaviour of the intensity process. To manage a PPR model, two new objects have been introduced. The first object belongs to yuima.PPR-class, contains the mathematical structure of a PPR model and eventually the dataset. The last object belongs to the yuima.PPR.qmle-class and is filled with a dataset, the model description and the estimated parameters obtained from the considered dataset. We discuss also how to use these objects to manage the CARMA-Hawkes process recently proposed in actuarial science to model the insurance claims. The CARMA-Hawkes process is a generalization of the standard Hawkes where the exponential kernel is substituted by the CARMA kernel. The main advantage of this model is its ability to reproduce a more complex dependence structure compared with the autocovariance generated by the Hawkes process.
