We derive the asymptotic distributions of degenerate <InlineEquation ID="IEq7"> <EquationSource Format="TEX">$$U$$</EquationSource> </InlineEquation>- and <InlineEquation ID="IEq8"> <EquationSource Format="TEX">$$V$$</EquationSource> </InlineEquation>-statistics of stationary and ergodic random variables. Statistics of these types naturally appear as approximations of test statistics. Since the limit variables are of complicated structure, typically depending on unknown...</equationsource></inlineequation></equationsource></inlineequation>

We provide a consistent specification test for GARCH(1,1) models based on a test statistic of Cramér-von Mises type. Since the limit distribution of the test statistic under the null hypothesis depends on unknown quantities in a complicated manner, we propose a model-based...

In this paper, we propose a model-free bootstrap method for the empirical process under absolute regularity. More precisely, consistency of an adapted version of the so-called dependent wild bootstrap, that was introduced by Shao (2010) and is very easy to implement, is proved under minimal...