Functional ANOVA-type methods with interpretable visualization for comparisons among groups of time series
Caragea, Petruta Berg, Emily De Brabanter, Kris Hofmann, Heike Nordman, Dan
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Data sampled densely in space and time have become increasingly abundant as a result of advances in modern technology. However, the presence of complex dependence and current computational limitations have made many classical inferential approaches practically infeasible. In this work, we develop an ANOVA-type method for functional data that allows comparisons among groups of time series with complex spatio-temporal dependence. This work is innovative as it 1) proposes a flexible framework that accommodates a variety of tests in the ANOVA setting, 2) introduces a novel and interpretable visualization, and 3) considers spatially correlated time series. Due to its flexibility, this method is widely applicable to scientific domains where data are naturally grouped and displays complex spatio-temporal dependence. We motivate and illustrate the utility of this method in the context of three applications. In the first, we study the effects of experimentally simulated climate change on soil temperatures. As extreme cold temperatures can have adverse effects on plant growth, quantifying the effect of climate change on daily minimum soil temperatures can signify phenological changes in high-elevation areas. In the second, we study the effect of social context on avian thermoregulation by comparing avian body temperature when house sparrows are housed among healthy and sick sparrows. In the third, we detect differences in photosynthetic activity between two vegetative areas in California using satellite measurements of solar-induced chlorophyll fluorescence (SIF). A simulation study illustrates the performance of the methods in various experimental contexts. The proposed functional ANOVA methodology provides robust and interpretable tests for identifying differences between groups of curves, with broad applications to physical, environmental and life sciences.