Parametric estimation of a bivariate stable Lévy process

Parametric estimation of a bivariate stable Lévy process

We propose a parametric model for a bivariate stable Lévy process based on a Lévy copula as dependence model. We estimate the parameters of the full bivariate model by maximum likelihood estimation. As observation scheme we assume that we observe all jumps larger than some ε > 0 and base our statistical analysis on the resulting compound Poisson process. We derive the Fisher information matrix ...

Parametric estimation of the driving Lévy process of multivariate CARMA processes from discrete observations

We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0, h, 2h, . . .). Beginning with a new state space representation, we develop a method to recover the driving Lévy process exactly from a continuous record of the observed MCARMA process. We use tools fro...

Estimation of Linear Functionals of Bivariate Distributions with Parametric Marginals

Parameter estimation of a bivariate compound Poisson process

In this article, we review the concept of a Lévy copula to describe the dependence structure of a bivariate compound Poisson process. In this first statistical approach we consider a parametric model for the Lévy copula and estimate the parameters of the full dependent model based on a maximum likelihood approach. This approach ensures that the estimated model remains in the class of multivaria...

Estimation of Count Data using Bivariate Negative Binomial Regression Models

Abstract Negative binomial regression model (NBR) is a popular approach for modeling overdispersed count data with covariates. Several parameterizations have been performed for NBR, and the two well-known models, negative binomial-1 regression model (NBR-1) and negative binomial-2 regression model (NBR-2), have been applied. Another parameterization of NBR is negative binomial-P regression mode...