L2-NED condition and the Functional Central Limit Theorem for certain type of ARCH(∞) model

Abstract

본 논문에서는 hyperbolic memory를 가지는 ARCH 모형과 geometric memory를 가지는 ARCH 모형을 대상으로 Functional Central Limit Theorem (FCLT) 이 성립하는 조건을 찾는다. 이를 위해 L2-NED (Near Epoch Dependence)의 관점을 이용하고 et의 2차 모멘트의 존재성을 가정하였다.;Asymptotic convergence theories such as the central limit theorem (CLT) and the functional central limit theorem (FCLT) are crucial for statistical inference in time series. In this paper, we consider the L2-NED condition and the Functional Central Limit Theorem in specific time series models. Especially, ARCH model with hyperbolic memory (HYGARCH model) and ARCH model with geometric memory are considered.