Inference for Near-Integrated Time Series with Infinite Variance
无限方差近单位根时间序列的统计推断AI 解读 ↓
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AI 根据所提供的论文材料归类：摘要明确研究近单位根自回归时间序列、重尾创新及其渐近推断，直接对应时间序列方法方向。
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无限方差近单位根时间序列的统计推断
- 研究问题
- 当近单位根自回归序列的噪声具有无限方差时，最小二乘估计的极限分布如何变化，有限方差推断为何不再适用？
- 方法与思路
- 作者研究噪声属于稳定律吸引域的近单位根一阶自回归模型，利用弱收敛与涉及 Lévy 过程的随机积分建立渐近理论。
- 材料陈述的贡献
- 摘要称建立了自回归系数最小二乘估计的渐近分布，并为重尾噪声下进一步研究单位根检验和协整提供理论基础。
- 阅读关注点
- 应核对近单位根参数的渐近设定、稳定律吸引域及噪声依赖条件，并区分已证明的估计结论与后续检验应用。
- 阅读边界
- 仅据 OpenAlex 索引摘要，稿件版本未注明；未给出具体检验、临界值或有限样本表现，不能把潜在应用视为完整检验方案。
原文摘要
An autoregressive time series is said to be near-integrated (nearly nonstationary) if some of its characteristic roots are close to the unit circle. Statistical inference for the least squares estimators of near-integrated AR(1) models has been under rigorous study recently both in the statistics and econometric literatures. Although classical asymptotics are no longer available, through the study of weak convergence of stochastic processes, one can establish the asymptotic theories in terms of simple diffusion processes or Brownian motions. Such results rely heavily on the finiteness of the variance of the noise. When this finite variance condition fails, whereas many physical and economic phenomena are believed to be generated by an infinite variance noise sequence, the aforementioned asymptotics are not applicable. In this article, a unified theory concerning near-integrated autoregressive time series with infinite variance is developed. In particular, when the noise sequence {ε t } belongs to the domain of attraction of a stable law with index α (0 < α < 2), that is, heavy-tailed, the asymptotic distribution of the least squares estimate of the autoregressive coefficient of a near-integrated AR(1) model is established. Instead of Brownian motions, weak convergence theory and stochastic integral involving Lévy processes are required to handle the infinite variance case. Results developed in this article not only provide an analog parallel to the finite variance model, but also allow one to study issues involving unit root tests and cointegrations where the underlying time series is generated by a heavy-tailed noise sequence.