Title: New classes and methods in YUIMA
Authors: Lorenzo Mercuri - University of Milan (Italy) [presenting]
Abstract: Some advances in the implementation of advanced mathematical tools in the Yuima package are presented. First, we discuss a new class called yuima.law that refers to the mathematical description of a general Levy process used in the formal definition of a general Stochastic Differential Equation. The final aim is to have an object, defined by the user, that contains all possible information about the Levy process considered. This class creates a link between Yuima and other R packages that manage specific Levy process like for example ghyp or MixedTS available on CRAN. The second class, that we discuss, is the yuima.PPR that refers to the mathematical description of the Point Process Regression Model. This model can be seen as a generalization of a self-exciting point process, since it is possible to consider external covariates in the intensity process. We discuss the implemented methods for the definition, simulation and estimation of these processes.We also discuss the exact maximum likelihood estimation procedure for a Levy CARMA model. The new method is based on the existence of an analytical expression for the characteristic function of a general Levy CARMA model. We show that we are able to overcome the problems that arise in the estimation procedure based on Kalman Filter that requires the existence of the second moment for the underlying Levy process. Real and simulated examples are shown.