Gaussian approximation for nonstationary time series with optimal rate and explicit construction
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非平稳时间序列的最优速率高斯逼近与显式构造
- 研究问题
- 如何为非平稳时间序列提供可构造且可实施的高斯逼近，以支持非平稳误差下的变点检测和同时推断？
- 方法与思路
- 作者给出两条高斯逼近构造路径，一条偏重理论自然性，另一条强调实际可实施性，并据此发展推断方法。
- 材料陈述的贡献
- 摘要称逼近适用于广泛的非平稳序列并达到最优速率，进一步给出变点检测与同时推断理论及模拟、数据分析。
- 阅读关注点
- 应核对允许的非平稳性与依赖条件、最优速率的比较标准，以及可实施构造中的估计步骤和误差控制。
- 阅读边界
- 依据 arXiv 预印本摘要，不能据此声称已同行评审或期刊接收；具体条件与速率未说明，也不推断刊本变化。
原文摘要
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of independence and/or stationarity at its best. The main obstacle is that the existing Gaussian approximation results for non-stationary processes only provide an existential proof and thus they are difficult to apply. In this paper, we provide two clear paths to construct such a Gaussian approximation for non-stationary series. While the first one is theoretically more natural, the second one is practically implementable. Our Gaussian approximation results are applicable for a very large class of non-stationary time series, obtain optimal rates and yet have good applicability. Building on such approximations, we also show theoretical results for change-point detection and simultaneous inference in presence of non-stationary errors. Finally we substantiate our theoretical results with simulation studies and real data analysis.