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Derivatives and Fisher information of bivariate copulas. (English) Zbl 1297.62046

Summary: Data sets with complex relationships between random variables are increasingly studied in statistical applications. A popular approach to model their dependence is the use of copula functions. Our contribution is to derive expressions for the observed and expected information for several bivariate copula families, in particular for the Student’s \(t\)-copula. Further likelihood derivatives which are required for numerical implementations are computed and a numerically stable implementation is provided in the R-package VineCopula. Using a real world data set of stock returns, we demonstrate the applicability of our approach for the routinely calculation of standard errors. In particular, we illustrate how this prevents overestimating the time-variation of dependence parameters in a rolling window analysis.

MSC:

62F10 Point estimation
62F12 Asymptotic properties of parametric estimators
62F99 Parametric inference
62H05 Characterization and structure theory for multivariate probability distributions; copulas

Software:

R; VineCopula; beta.der
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References:

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