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Title: Testing normality of functional time series Authors:  Siegfried Hoermann - Univ libre de Bruxelles (Belgium) [presenting]
Piotr Kokoszka - Colorado State University (USA)
Lajos Horvath - University of Utah (USA)
Tomasz Gorecki - Adam Mickiewicz University (Poland)
Abstract: Tests of normality for a time series of functions are developed. The tests are related to the commonly used Jarque Bera test. The assumption of normality has played an important role in many methodological and theoretical developments in the field of functional data analysis, yet, no inferential procedures to verify it have been proposed so far, even for iid functions. We propose different approaches and evaluate the tests via simulations. For the test which gives the best size and power trade-off we establish large sample validity under general conditions. We obtain interesting insights by applying them to pollution and intraday price curves. While the pollution curves can be treated as normal, the normality of high frequency price curves is rejected.