This paper considers the effect of least squares procedures for nearlyunstable linear time series with strongly dependent innovations. Under ageneral framework and appropriate scaling, it is shown that ordinary leastsquares procedures converge to functionals of fractional Ornstein--Uhlenbeckprocesses. We use fractional integrated noise as an example to illustrate theimportant ideas. In this case, the functionals bear only formal analogy tothose in the classical framework with uncorrelated innovations, with Wienerprocesses being replaced by fractional Brownian motions. It is also shown thatlimit theorems for the functionals involve nonstandard scaling and nonstandardlimiting distributions. Results of this paper shed light on the asymptoticbehavior of nearly unstable long-memory processes.
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