Department of Epidemiology and Biostatistics, School of Public Health, University at Albany, State University of New York, Rensselaer, New York, United States of America.
PLoS One. 2024 Sep 17;19(9):e0310563. doi: 10.1371/journal.pone.0310563. eCollection 2024.
This research introduces a novel approach to resampling periodically correlated time series using bandpass filters for frequency separation called the Variable Bandpass Periodic Block Bootstrap 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 periodically correlated time series. Existing extensions of the block bootstrap help preserve the correlation structures of periodically correlated processes but suffer from flaws and inefficiencies. Analyses of time series data containing cyclic, seasonal, or periodically correlated principal components often seen in annual, daily, or other cyclostationary processes benefit from separating these components. The Variable Bandpass Periodic Block Bootstrap uses bandpass filters to separate a periodically correlated component from interference such as noise at other uncorrelated frequencies. A simulation study is presented, demonstrating near universal improvements obtained from the Variable Bandpass Periodic Block Bootstrap when compared with prior block bootstrapping methods for periodically correlated time series.
本研究提出了一种使用带通滤波器对周期性相关时间序列进行频率分离的重采样方法，称为可变带通周期块自举法，然后检验了这种新方法的显著优势。自举法通过对原始数据进行有放回的重采样来估计统计量的抽样分布，而块自举法是一种无模型的相关时间序列数据重采样策略，但它们都不能保留周期性相关时间序列中的相关性。现有的块自举法扩展有助于保留周期性相关过程的相关结构，但存在缺陷和效率低下的问题。对包含周期性相关主成分的时间序列数据的分析，这些主成分通常出现在年度、每日或其他周期性平稳过程中，受益于将这些成分分离。可变带通周期块自举法使用带通滤波器将周期性相关分量与其他不相关频率的干扰（如噪声）分离。本文提出了一项模拟研究，结果表明，与先前用于周期性相关时间序列的块自举法相比，可变带通周期块自举法几乎普遍提高了性能。
