Liudas Giraitis

TL;DR: In this paper, a central limit theorem for quadratic forms in strongly dependent linear (or moving average) variables is proved, generalizing the results of Avram [1] and Fox and Taqqu [3] for Gaussian variables.

TL;DR: In this paper, a rescaled variance test based on V/S statistic was proposed for general fourth order stationary sequences, which is shown to have a simpler asymptotic distribution and to achieve a somewhat better balance of size and power than Lo's modified R/S test and the KPSS test of Kwiatkowski et al.

TL;DR: In this article, a broad class of nonnegative ARCH(∞) models is studied and sufficient conditions for the existence of a stationary solution are established and an explicit representation of the solution as a Volterra type series is found under their assumptions, the covariance function can decay slowly like a power function, falling just short of the long memory structure.

TL;DR: Introduction Estimation Some Inference Problems Residual Empirical Processes Regression Models Nonparametric Regression with Heteroscedastic Errors Model Checking under Long Memory Long Memory under Infinite Variance.

TL;DR: Conditions for the CLT for non-linear functionals of stationary Gaussian sequences are discussed, with special references to the borderline between the CLTs and the non-CLTs as discussed by the authors.