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A0969
Title: Pivotal tests for relevant differences in the second order dynamics of functional time series Authors:  Anne van Delft - Columbia University (United States) [presenting]
Holger Dette - Ruhr-Universitaet Bochum (Germany)
Abstract: Motivated by the need to statistically quantify differences between modern (complex) data sets which commonly result in high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to detect relevant differences between the second-order dynamics of two functional time series. In order to take into account the between-function dynamics that characterize this type of functional data, a frequency domain approach is taken. Test statistics are developed to compare differences in the spectral density operators and in the primary modes of variation as encoded in the associated eigenelements. Under mild moment conditions, we show convergence of the underlying statistics to Brownian motions and construct pivotal test statistics. The latter is essential because the nuisance parameters can be unwieldy and their robust estimation infeasible, especially if the two functional time series are dependent. In addition to these novel features, the properties of the tests are robust to any choice of frequency band enabling also to compare energy contents at a single frequency. The finite sample performance of the tests is verified through a simulation study and is illustrated with an application to fMRI data.