We deduce a partial version of the KMT (1975) inequality for coupling the uniform empirical process with a sequence of Brownian bridges via the construction used by Cs¨org?o and R´ev´esz (CsR) (1978) for their similar coupling of the uniform quantile process with another sequence of Brownian...

In this paper we study strong approximations (invariance principles) of the sequential uniform and general Bahadur-Kiefer processes of long-range dependent sequences. We also investigate the strong and weak asymptotic behavior of the sequential Vervaat process, i.e., the integrated sequential...

This paper is concerned with weak convergence together with convergence rates in weighted almost sure local central limit theorems for random walks. The main tools are stochastic calculus and strong approximations.

We establish the strong consistency and the asymptotic normality of the variance-targeting estimator (VTE) of the parameters of the multivariate CCC-GARCH($p,q$) processes. This method alleviates the numerical difficulties encountered in the maximization of the quasi likelihood by using an...

We show that the empirical process of the squared residuals of an ARCH(p) sequence converges in distribution 1,0 a Gaussirm process B(F(t)) +t f(t) e, where F is the distribution function of the squared innovations, f its derivative, {B(tl, 0 <; t>1} a Brownian bridge and e a normal random variable.