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

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].