周期相关时间序列与可变带通周期块自助法
Periodically Correlated Time Series and the Variable Bandpass Periodic Block Bootstrap
AI总结：
针对周期相关时间序列，提出可变带通周期块自助法（VBPBB），利用带通滤波器分离频率成分，模拟实验显示其优于现有块自助法。
摘要：
本研究提出了一种对周期相关（PC）时间序列进行重采样的新方法，该方法利用带通滤波器进行频率分离，称为可变带通周期块自助法（VBPBB），并考察了该新方法的显著优势。虽然自助法通过有放回地重采样原始数据来估计统计量的抽样分布，而块自助法是一种针对相关时间序列数据的无模型重采样策略，但两者均无法保留PC时间序列中的相关性。现有的块自助法扩展有助于保留PC过程的相关结构，但存在缺陷和低效问题。对包含循环、季节性或PC主成分的时间序列数据（常见于年度、日度或其他循环平稳过程）进行分析时，分离这些成分是有益的。VBPBB利用带通滤波器将PC成分与噪声等其他不相关频率上的干扰分离开来。本文展示了一项模拟研究，证明与先前针对周期相关时间序列的块自助法相比，VBPBB在几乎所有情况下均带来了改进。
英文摘要：
This research introduces a novel approach to resampling periodically correlated (PC) time series using bandpass filters for frequency separation called the Variable Bandpass Periodic Block Bootstrap (VBPBB) and then examines the significant advantages of this new method. While bootstrapping allows estimation of a statistic's sampling distribution by resampling the original data with replacement, and block bootstrapping is a model-free resampling strategy for correlated time series data, both fail to preserve correlations in PC time series. Existing extensions of the block bootstrap help preserve the correlation structures of PC processes but suffer from flaws and inefficiencies. Analyses of time series data containing cyclic, seasonal, or PC principal components often seen in annual, daily, or other cyclostationary processes benefit from separating these components. The VBPBB uses bandpass filters to separate a PC component from interference such as noise at other uncorrelated frequencies. A simulation study is presented, demonstrating near universal improvements obtained from the VBPBB when compared with prior block bootstrapping methods for periodically correlated time series.
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