# 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…
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• Mathematics
Scandinavian Journal of Statistics
• 2021
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• Mathematics
Scandinavian Journal of Statistics
• 2019
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• Mathematics
• 2017
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• Mathematics
• 2019
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• Mathematics
• 2015
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• Mathematics
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• 2014
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• Mathematics
• 2015
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Geometric ergodicity of the multivariate COGARCH(1,1) process
• Mathematics
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• 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

## References

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We suggest moment estimators for the parameters of a continuous time GARCH(1,1) process based on equally spaced observations. Using the fact that the increments of the COGARCH(1,1) process are
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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.
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GARCH is one of the most prominent nonlinear time series models, both widely applied and thoroughly studied. Recently, it has been shown that the COGARCH model, which has been introduced a few years