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Higher moments and prediction-based estimation for the COGARCH(1,1) model. (English) Zbl 1372.62037

Summary: 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 simulation study shows that the method of prediction-based estimating function outperforms the other available estimation methods.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M05 Markov processes: estimation; hidden Markov models
62P05 Applications of statistics to actuarial sciences and financial mathematics
60H10 Stochastic ordinary differential equations (aspects of stochastic analysis)

Software:

R; Mathematica
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References:

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