Higher Moments and Prediction Based Estimation for the COGARCH(1,1) model
Abstract
COGARCH models are continuous time version of the well known GARCH models of financial returns. They are solution of a stochastic differential equation driven by a L\'evy process. The first aim of this paper is to show how the method of Prediction-Based Estimating Functions (PBEFs) can be applied to draw statistical inference from a discrete sample of observations of a COGARCH(1,1) model as far as the higher order structure of the process is clarified. Motivated by the search for an optimal PBEF, a second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process, whenever they exist. Asymptotic results are given and a simulation study shows that the method of PBEF outperforms the other available estimation methods.
Cite
@article{arxiv.1401.7819,
title = {Higher Moments and Prediction Based Estimation for the COGARCH(1,1) model},
author = {Enrico Bibbona and Ilia Negri},
journal= {arXiv preprint arXiv:1401.7819},
year = {2014}
}