摘要翻译：
本文研究了具有强相依新息的近似不稳定线性时间序列的最小二乘法的影响。在一般框架和适当尺度下，证明了普通最小二乘过程收敛于分数阶Ornstein-Uhlenbeck过程的泛函。我们以分数积分噪声为例来说明其中的重要思想。在这种情况下，函数与经典框架中的函数只有形式上的类比，具有不相关的新息，维纳过程被分数布朗运动所取代。本文还证明了泛函的极限定理涉及非标准标度和非标准极限分布。本文的结果揭示了近不稳定长记忆过程的渐近性态。
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英文标题：
《Asymptotic theory of least squares estimators for nearly unstable
  processes under strong dependence》
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作者：
Boris Buchmann, Ngai Hang Chan
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  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.
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PDF链接：
https://arxiv.org/pdf/711.3589