This study reflects on the inconsistency of the fixed-design residual bootstrap procedure for GARCH models under dependent innovations. We introduce a novel recursive-design residual block bootstrap procedure to accurately quantify the uncertainty around parameter estimates and volatility...

For order statistics Xi,n,Xj,n,Xk,n with 1[less-than-or-equals, slant]i<j<k[less-than-or-equals, slant]n, and an independent beta distributed random variable C the distributional equation is established for uniform distributions as well as seen to be characteristic.

This paper questions whether it is possible to derive consistency and asymptotic normality of the Gaussian quasi-maximum likelihood estimator (QMLE) for possibly the simplest VEC-GARCH model, namely the multivariate ARCH(1) model of the BEKK form, under weak moment conditions similar to the...

The classical functional delta method (FDM) provides a convenient tool for deriving the asymptotic distribution of statistical functionals from the weak convergence of the respective empirical processes. However, for many interesting functionals depending on the tails of the underlying...

We consider a multi-asset discrete-time model of a financial market with proportional transaction costs as described by Schachermayer [7]. In this model, the set of all self-financing trading strategies contains for example trading strategies which consist of buying an asset and selling it at...

We present two general results that can be used to obtain asymptotic properties for statistical functionals based on linear long-memory sequences. As examples for the first one we consider L- and V-statistics, in particular tail-dependent L-statistics as well as V-statistics with unbounded...