非平稳时间序列局部部分和的泛函中心极限定理
A Functional Central Limit Theorem for Localized Partial Sums of Non-Stationary Time Series
浏览论文内容
中文总结 AI 辅助
研究非平稳时间序列局部部分和的泛函中心极限定理，通过核加权等方法，在特定条件下证明局部过程弱收敛到高斯分布，可扩展到特定空间，还用于非参数回归检验，展示了方法的性能和适用性。
中文摘要 AI 辅助
本文在物理相依性测度几何衰减条件下，为分段局部平稳时间序列的核加权部分和过程建立了局部泛函中心极限定理。证明了局部过程在\(D'(0,1)\)中弱收敛到中心高斯随机分布，该极限自然扩展到\(L^2([0,1])\)上的等正态高斯过程。还推导了由\(L^2([0,1])\)的全有界子集索引的过程的弱收敛。作为应用，用于非参数回归中针对线性、多项式和一般备择假设的常数均值函数检验。模拟结果和数据示例说明了该方法的有限样本性能和实际适用性。
英文摘要
A localized functional central limit theorem is established for kernel-weighted partial sum processes of piecewise locally stationary time series under geometric decay of the physical dependence measure. The localized process is shown to converge weakly to a centered Gaussian random distribution in $D'(0,1)$, and the limit extends naturally to an isonormal Gaussian process on $L^2([0,1])$. Weak convergence is further derived for processes indexed by totally bounded subsets of $L^2([0,1])$. As an application, the localized limit theory is used to construct tests for constant mean functions against linear, polynomial, and general alternatives in non-parametric regression with locally stationary errors. Simulation results and data examples illustrate the finite sample performance and practical applicability of the proposed methodology.
