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Abstract:
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When time series data contain frequency specific principal components, including periodic ‘signals’ such as seasonal or daily cycles, separating these components from interfering frequencies is essential to understand the time and space structures of variation within data. Without properly separating processes operating at different frequencies, statistical analysis can obscure and confound true spatio-temporal relationships. Kolmogorov-Zurbenko (KZ) filters are iterated moving averages and their extensions are well suited to spatio-temporal analysis by frequency separation (STAFS). With guided parameter selection, KZ filters permit finely separating adjacent uncorrelated frequencies and enable analysis of factors within each independent component time scale. This work derives formulas for the separable spectral distance between any two frequencies given data constraints as well as sequence length requirements for frequency separation within research design. Finally, simulations demonstrate proper guided spatio-temporal component frequency separation, the consequences of incomplete signal separation, and effectiveness of this method in spatial, temporal, and spatio-temporal analysis.
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