  This paper develops the asymptotic theory for parametric and nonparametric
regression models when the errors have a fractional local to unity root (FLUR)
model structure. FLUR models are stationary time series with semi-long range
dependence property in the sense that their covariance function resembles that
of a long memory model for moderate lags but eventually diminishes
exponentially fast according to the presence of a decay factor governed by a
noncentrality parameter. When this parameter is sample size dependent, the
asymptotic normality for these regression models admit a wide range of
stochastic processes with behavior that includes long, semi-long, and short
memory processes.
