A GENERAL LIMIT THEORY FOR NONLINEAR FUNCTIONALS OF NONSTATIONARY TIME SERIES
非平稳时间序列非线性泛函的一般极限理论AI 解读 ↓
← 返回论文列表与筛选
阅读说明
本页整理公开书目信息，不生成学术质量评分。AI 解读根据题名及所注明的摘要或原文片段生成，未完成全文核验，可能有误；具体假设、证明与结论请核对原文。摘要保留来源文本，未经模型改写。
DOI 首次登记不等于接收或发表日期。部分更正、评论等条目没有独立摘要；缺少可靠材料时保留待补状态。
引用量采用 OpenAlex 单条关联记录，不合计多个记录；关联记录可能包含正式发表版本，不等于此版本单独引用。缺失不视为零，引用指标不代表论文质量。
关注作者按书目中的完整姓名匹配，同名和姓名变体需人工辨别。相关论文先按共享细分方向和具体方法排列，再参考通用方法与发表日期。
分类依据与纠错
AI 根据所提供的论文材料归类：摘要明确涉及单位根、局部单位根、分数过程及非平稳回归的极限理论，直接对应时间序列方向。
反馈分类问题
正在核对关联版本…
代码、数据与补充材料
正在核对对应版本的资源…
关注这篇论文的作者
非平稳时间序列非线性泛函的一般极限理论
- 研究问题
- 涉及平稳与非平稳序列的样本方差、协方差泛函具有何种极限分布，长记忆为何会使常规自归一化统计量呈现双峰？
- 方法与思路
- 作者建立适用于参数和非参数回归的极限理论，分析常规自归一化统计量的双峰行为，并提出新的自归一化检验统计量。
- 材料陈述的贡献
- 摘要称，平稳长记忆下双峰可持续至很大样本，非平稳长记忆下甚至出现在极限分布中；新统计量改善了推断近似。
- 阅读关注点
- 应核对单位根、局部单位根及分数过程各自的条件，厘清有限样本双峰与极限双峰的区别，并检查新归一化的构造和证据。
- 阅读边界
- 仅据所给 Crossref 版本摘要，无法确定过程参数范围、归一化公式及近似改善的幅度，也不能推断其他版本的变化。
原文摘要
New limit theory is provided for a wide class of sample variance and covariance functionals involving both nonstationary and stationary time series. Sample functionals of this type commonly appear in regression applications and the asymptotics are particularly relevant to estimation and inference in nonlinear nonstationary regressions that involve unit root, local unit root, or fractional processes. The limit theory is unusually general in that it covers both parametric and nonparametric regressions. Self-normalized versions of these statistics are considered that are useful in inference. Numerical evidence reveals interesting strong bimodality in the finite sample distributions of conventional self-normalized statistics similar to the bimodality that can arise in t -ratio statistics based on heavy tailed data. Bimodal behavior in these statistics is due to the presence of long memory innovations and is shown to persist for very large sample sizes even though the limit theory is Gaussian when the long memory innovations are stationary. Bimodality is shown to occur even in the limit theory when the long memory innovations are nonstationary. To address these complications, new self-normalized versions of the test statistics are introduced that deliver improved approximations that can be used for inference.