We study subsampling estimators for the limit variance σ2=V ar(X1)+2∑k=2∞Cov(X1,Xk) of partial sums of a stationary stochastic process (Xk)k≥1. We establish L2-consistency of a non-overlapping block resampling method. Our results apply to processes that can be represented as functionals...

We derive the asymptotical distributions of two-sample U-statistics and two-sample empirical U-quantiles in the case of weakly dependent data. Our results apply to observations that can be represented as functionals of absolutely regular processes, including e.g. many classical time series...

Statistical methods for functional data are of interest for many applications. In this paper, we prove a central limit theorem for random variables taking their values in a Hilbert space. The random variables are assumed to be weakly dependent in the sense of near epoch dependence, where the...

A CUSUM type test for constant correlation that goes beyond a previously suggested correlation constancy test by considering Spearman’s rho in arbitrary dimensions is proposed. Since the new test does not require the existence of any moments, the applicability on usually heavy-tailed financial...

In this paper we investigate the problem of detecting a change in the drift parameters of a generalized Ornstein–Uhlenbeck process which is defined as the solution of <Equation ID="Equ23"> <EquationSource Format="TEX">$$\begin{aligned} dX_t=(L(t)-\alpha X_t) dt + \sigma dB_t \end{aligned}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink" display="block"> <mrow> <mtable columnspacing="0.5ex"> <mtr> <mtd columnalign="right"> <mrow> <mi>d</mi> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo>=</mo> <mrow> <mo stretchy="false">(</mo> <mi>L</mi> <mrow> <mo stretchy="false">(</mo> <mi>t</mi> <mo stretchy="false">)</mo> </mrow> <mo>-</mo> <mi mathvariant="italic">α</mi> <msub> <mi>X</mi> <mi>t</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mi>d</mi> <mi>t</mi> <mo>+</mo> <mi mathvariant="italic">σ</mi>...</mrow></mtd></mtr></mtable></mrow></math></equationsource></equationsource></equation>

We propose a new test against a change in correlation at an unknown point in time based on cumulated sums of empirical correlations. The test does not require that inputs are independent and identically distributed under the null. We derive its limiting null distribution using a new functional...

Associated sequences have been studied extensively in recent years. Burton et al. (1986) introduced a generalization of association to d-dimensional random vectors and proved Functional Central Limit Theorems. In the present paper a Berry-Esséen theorem and a Functional Law of the Iterated...

We present a new technique for proving the empirical process invariance principle for stationary processes (Xn)n=0. The main novelty of our approach lies in the fact that we only require the central limit theorem and a moment bound for a restricted class of functions (f(Xn))n=0, not containing...