# Higher Moments and Prediction‐Based Estimation for the COGARCH(1,1) Model

```@article{Bibbona2014HigherMA,
title={Higher Moments and Prediction‐Based Estimation for the COGARCH(1,1) Model},
author={Enrico Bibbona and Ilia Negri},
journal={Scandinavian Journal of Statistics},
year={2014},
volume={42},
pages={891 - 910}
}```
• Published 30 January 2014
• Mathematics
• Scandinavian Journal of Statistics
COGARCH models are continuous time versions of the well‐known GARCH models of financial returns. The first aim of this paper is to show how the method of prediction‐based estimating functions can be applied to draw statistical inference from observations of a COGARCH(1,1) model if the higher‐order structure of the process is clarified. A second aim of the paper is to provide recursive expressions for the joint moments of any fixed order of the process. Asymptotic results are given, and a…
Moment‐based estimation for the multivariate COGARCH(1,1) process
• Mathematics
Scandinavian Journal of Statistics
• 2021
For the multivariate COGARCH process, we obtain explicit expressions for the second‐order structure of the “squared returns” process observed on an equidistant grid. Based on this, we present a
COGARCH models: some applications in finance
The aim of this paper is to show how the method of Prediction-Based Estimating Functions can be applied to estimate the parameters of a COGARCH(1,1) model from observations taken from real data set.
Indirect Inference for Lévy‐driven continuous‐time GARCH models
• Mathematics
Scandinavian Journal of Statistics
• 2019
We advocate the use of an Indirect Inference method to estimate the parameter of a COGARCH(1,1) process for equally spaced observations. This requires that the true model can be simulated and a
Indirect Inference for Lévy-Driven Continuous-Time GARCH Models
• Mathematics
• 2017
We advocate the use of an Indirect Inference method to estimate the parameter of a COGARCH process for equally spaced observations. This requires that the true model can be simulated and a reasonable
Simulation-based estimation of time series and stochastic volatility processes
• Mathematics
• 2019
This thesis investigates simulation-based methods to estimate time series processes. We apply Indirect Inference to estimate the parameter of a COGARCH(1,1) process. Then we develop new estimators
Fractionally integrated COGARCH processes
• Mathematics
• 2015
We construct fractionally integrated continuous-time GARCH models, which capture the observed long range dependence of squared volatility in high-frequency data. Since the usual Molchan-Golosov and
Asymmetric COGARCH processes
• Mathematics
J. Appl. Probab.
• 2014
Higher order moments are calculated and the first jump approximation is extended, prerequisites for moment estimation and pseudo maximum likelihood estimation of the GJR-COGARCH parameters, respectively, which are derived in detail.
COGARCH Processes: Theory and Asymptotics for the Pseudo-Maximum Likelihood Estimator
In order to capture the so-called stylized facts and model high-frequency and irregularly time spaced financial data continuous time GARCH processes are becoming popular. In 2004 Kluppelberg, Lindner
Estimation and Simulation of a COGARCH(p,q) model in the YUIMA project
• Mathematics
• 2015
In this paper we show how to simulate and estimate a COGARCH(p,q) model in the R package yuima. Several routines for simulation and estimation are available. Indeed for the generation of a
Geometric ergodicity of the multivariate COGARCH(1,1) process
• Mathematics
Stochastics
• 2020
ABSTRACT For the multivariate COGARCH(1,1) volatility process we show sufficient conditions for the existence of a unique stationary distribution, for the geometric ergodicity and for the finiteness