  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.
