Frequency Separated Periodic Block Bootstrapping: Consistency and Robustness for Periodic Characteristics of Time Series

• Activity Number: 277 - SPEED: Biometrics and Environmental Statistics Part 1
• Type: Contributed
• Date/Time: Tuesday, August 9, 2022 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Edward Valachovic*
• Companies: University at Albany, State University of New York
• Keywords: Spatio – Temporal Analysis Frequency Separation; Frequency Separated Periodic Block Bootstrap; Periodically Correlated Time Series; Cyclostationary Process Frequency Interference; Seasonal Mean and Periodic characteristics; Kolmogorov-Zurbenko Iterated Moving Average

Abstract

The analysis of time series data composed of multiple cyclostationary processes, including seasonality or other periodically correlated (PC) components, benefits from the separation of these PC components from interference at different frequencies. Block bootstrapping strategies, which preserve the correlation structure of a given PC process but destroys any others at different frequencies, may then be used to investigate the periodic characteristics of each PC processes within the time series. Frequency separation permits estimation of each PC statistic’s sampling distribution as well as reconstruction of the time series with multiple PC components preserving each correlation structure simultaneously. This method of Frequency Separated Periodic Block Bootstrapping (FSPBB) separates PC components by frequency prior to block bootstrapping the components. In this simulation study, the consistency and robustness of FSPBB for the estimation of the characteristics of PC components is shown across a range of PC frequency, PC component signal frequency separation, and interfering noise. FSPBB performance is compared against block bootstrapping in the absence of frequency separation.