Adaptive Estimators and Tests of Stationary and Nonstationary Short- and Long-Memory ARFIMA–GARCH Models
平稳与非平稳短长记忆 ARFIMA–GARCH 模型的自适应估计与检验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：摘要研究分数整合、长记忆、自回归与单位根，并应用于通胀序列，最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
平稳与非平稳短长记忆 ARFIMA–GARCH 模型的自适应估计与检验
- 研究问题
- 对于含 GARCH 误差的平稳或非平稳 ARFIMA 模型，未知残差密度下如何构建有效估计，并检验整数与分数单位根？
- 方法与思路
- 作者以统一框架研究局部渐近正态性、效率与极小极大界，构造自适应及有效估计量和 Wald 检验，并开展模拟与通胀应用。
- 材料陈述的贡献
- 摘要称，文章给出未知密度下的估计与检验理论，对称密度下构造 ARFIMA 参数的自适应估计，并报告美国通胀序列应用。
- 阅读关注点
- 应核对记忆参数范围、残差密度条件及各效率结论的区别，并检查单位根检验的局部备择、模拟设计和通胀模型诊断。
- 阅读边界
- 依据版本未注明的索引摘要；局部渐近正态性的参数范围记号不清，需查阅原PDF。完整条件和应用不确定性未说明，不能将通胀结论视为已独立验证。
原文摘要
This article considers the fractionally autoregressive integrated moving average [ARFIMA(p,d,q)] models with GARCH errors. The process generated by this model is short memory, long memory, stationary, and nonstationary, respectively, when d ∈ (-1/2, 0), d ∈ (0, 1/2), d ∈ (-1/2, 1/2), and d ∈ (1/2, ∞). Using a unified approach, the local asymptotic normality of the model is established for d ∈ ∪∞j = 0(J - 1/2, J + 1/2). The adaptivity and efficiency of the estimating parameters are discussed. In a class of loss functions, the asymptotic minimax bound of the estimators for the model is given when the density f of rescaled residuals is unknown. An adaptive estimator is constructed for the parameters in the ARFIMA part when f is symmetric, and a general form of the efficient estimator is also constructed for all the parameters in the ARFIMA and GARCH parts. When the density f is unknown, Wald tests are constructed for testing the unit root + 1 against the class of fractional unit roots. It is shown that these tests asymptotically follow the chi-squared distribution and are locally most powerful. These results are new contributions to the literature, even for the ARFIMA model with iid errors, except for the adaptive estimator in this case with d ∈ (0, 1/2). The performance of the asymptotic results in finite samples is examined through Monte Carlo experiments. An application to the U.S. Consumer Price Index inflation series is given, and a clear conclusion from this is that the series is neither an I(0) nor an I(1), but rather than an I(d) process with d ≈ 0.288.