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 an exponential tempering parameter. When this parameter is sample size dependent, the asymptotic theory for these regression models admit a wide range of stochastic processes with behavior that includes long, semi-long, and short memory processes.

当误差具有局部局部到统一根（FLUR）模型结构时，本文开发了参数和非参数回归模型的渐近理论。FLUR模型是具有半长距离依赖属性的平稳时间序列，从某种意义上说，它们的协方差函数类似于中度滞后的长记忆模型，但最终会根据存在由指数回火参数控制的衰减因子而以指数方式快速减小。当此参数取决于样本量时，这些回归模型的渐近理论会接受范围广泛的随机过程，其行为包括长，半长和短记忆过程。