Least squares estimators for nearly unstable processes for functionals of long-memory noises

Issue title: Statistical Methods for Decision Making and Risk Measures

Article type: Research Article

Authors: Chan, Ngai Hang^; | Liu, Wei Wei

Affiliations: Department of Statistics, Chinese University of Hong Kong, Shatin, NT, Hong Kong

Note: [] Corresponding author. E-mail: [email protected].

Abstract: This paper investigates the asymptotic theory of the least squares estimators (LSE) for a long-memory nearly unstable model when the innovation sequences are functionals of moving averages. It is shown that the limit distribution of the LSE is a functional of the Hermite Ornstein–Uhlenbeck process. This result not only generalizes the result of Buchmann and Chan [Ann. Statist. 35 (2007), 2001–2017], but also that of Wu [Economet. Theory 22 (2006), 1–14].

Keywords: Hermite Ornstein–Uhlenbeck processes, least squares estimator, long-memory noises, nearly unstable processes

DOI: 10.3233/RDA-2012-0066

Journal: Risk and Decision Analysis, vol. 3, no. 4, pp. 239-246, 2012