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.

翻译：本研究提出了一种新的重采样周期性相关时间序列的方法，利用带通滤波器进行频率分离，称为可变带通周期块状自助法，并探讨了该方法的显著优势。虽然自助法通过从原始数据中有放回地重采样来估计统计量的抽样分布，而块状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，但两者均无法保留周期性相关时间序列中的相关性。现有的块状自助法扩展有助于保持周期性相关过程的相关结构，但存在缺陷且效率低下。对于包含周期性、季节性或周期性相关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），分离这些成分有助于分析。可变带通周期块状自助法利用带通滤波器将周期性相关成分与噪声等其他非相关频率干扰分离。通过模拟研究，结果表明与先前的周期性相关时间序列块状自助方法相比，可变带通周期块状自助法几乎在所有情况下均表现出优越性。