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Title: Tests of independence of functional observations Authors:  Zdenek Hlavka - Charles University (Czech Republic) [presenting]
Marie Huskova - Charles University (Czech Republic)
Simos Meintanis - University of Athens (Greece)
Abstract: Statistical problems are often simplified by assuming independence of observations. Therefore, in real life applications, one should be able to test the validity of this assumption. We investigate general tests of independence in the framework of functional data, i.e., we test the null hypothesis that the observed random curves are independent. We note that existing procedures usually test only for lack of covariance, rather than independence and, for this reason, it makes sense to propose a new procedure based on characteristic functions (CF) that should be consistent against arbitrary deviations from the null hypothesis. After establishing basic asymptotic properties of the proposed CF-based test statistic, we discuss computational issues and investigate small sample properties of the CF-based test in a simulation study considering, e.g., functional autoregression, ARCH, and GARCH alternatives.