The serial dependency of multivariate financial data will often be filtered by considering the residuals of univariate GARCH models adapted to every single series. This is the correct filtering strategy if the multivariate process follows a so-called copula based multivariate dynamic model...

We generalize the results for statistical functionals given by [Fernholz, 1983] and [Serfling, 1980] to M estimates for samples drawn for an ergodic and stationary martingale sequence. In a first step, we take advantage of some recent results on the uniform convergency of the empirical...

We proof that Hadamard differentiability in addition with usual assumptions on the loss function for M estimates implies differentiability in quadratic mean. Thus both concepts are exchangeable. -- Hadamard differential ; Differentiability in quadratic mean

In this article, consistency and asymptotic normality of the quasi-maximum likelihood estimator (QMLE) in the class of polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extends the results of the standard GARCH model to the class...

In this article consistency and asymptotic normality of the quasi-maximum likelihood esti- mator (QMLE) in the class of polynomial augmented generalized autoregressive conditional heteroscedasticity models (GARCH) is proven. The result extend the results of (Berkes et al., 2003) and (Francq and...

We generalize the score test for time-varying copula parameters proposed by [Abegaz & Naik-Nimbalkar, 2008] to a setting where more than one-parametric copulas can be tested for time variation in at least one parameter. In a next step we model the daily log returns of the Commerzbank stock using...

There are several procedures to construct a skewed distribution. One of these procedures is based on a symmetric distribution that will be distorted by a skewed distribution defined on (0; 1). This proposal stems from Arellano-Valle et al. and was refined by Ferreira & Steel. Up to now, it is an...

There are several procedures to construct a skewed distribution. One of these procedures splits the value of a parameter of scale for the two halfs of a symmetric distribution. Fechner proposed this procedure in his famous book "Kollektivmaßlehre (1897), p. 295ff.". A similar proposal comes...

It is well known that the arithmetic mean of two possibly different copulas forms a copula, again. More general, we focus on the weighted power mean (WPM) of two arbitrary copulas which is not necessary a copula again, as different counterexamples reveal. However, various conditions regarding...

Keynes (1911) derived general forms of probability density functions for which the “most probable value” is given by the arithmetic mean, the geometric mean, the harmonic mean, or the median. His approach was based on indirect (i.e., posterior) distributions and used a constant prior...