  This paper considers the effect of least squares procedures for nearly
unstable linear time series with strongly dependent innovations. Under a
general framework and appropriate scaling, it is shown that ordinary least
squares procedures converge to functionals of fractional Ornstein--Uhlenbeck
processes. We use fractional integrated noise as an example to illustrate the
important ideas. In this case, the functionals bear only formal analogy to
those in the classical framework with uncorrelated innovations, with Wiener
processes being replaced by fractional Brownian motions. It is also shown that
limit theorems for the functionals involve nonstandard scaling and nonstandard
limiting distributions. Results of this paper shed light on the asymptotic
behavior of nearly unstable long-memory processes.
