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Abstract:
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This talk deals with two-sample tests for functional time series data with particular interest in finding out whether two sets of independent functional time series observations share the shape of their primary modes of variation. To this end, a novel approach in the relevant testing framework is introduced, where interest is not in testing an exact null hypothesis but rather in detecting deviations deemed sufficiently significant. The proposed test statistics rely on a self-normalization principle that helps avoid the notoriously difficult task of estimating the long-run covariance structure of the underlying functional time series. The main theoretical result is the derivation of the large-sample behavior of the proposed test statistics. Empirical evidence is provided through a simulation study, also comparing with competing methods, and an application to annual temperature data. The talk is based on joint work with Holger Dette (Ruhr University Bochum, Germany) and Greg Rice (University of Waterloo, Canada).
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