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Inference for the driving Lévy process of continuous-time moving average processes

Oberseminar Finanz- und Versicherungsmathematik


Inference for the driving Lévy process of continuous-time moving average processes

Abstract

Continuous-time moving average processes, defined as integrals of a deterministic kernel
function integrated with respect to a two sided Lévy process, provide a unifying framework
to different types of processes, including the popular examples of fractional Brownian
motion and fractional Lévy processes on the one side and Ornstein-Uhlenbeck processes
on the other side. The whole class of processes especially allows for a combination of a
given correlation structure with an infinitely divisible marginal distribution as it is desirable
for applications in finance, physics and hydrology.
So far inference for these processes is mainly concerned with estimating parameters
entering the kernel function which is responsible for the correlation structure. We now
consider the estimating problem for the driving Lévy process. We will provide two methods
working on different sets of conditions, one is based on a suitable integral transform, the
other on the Mellin transform.