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Anne Van Delft, UCLouvain Print
Thursday, 27 April 2017, 12:15 - 13:15

Anne Van Delft, UCLouvain

Testing for Stationarity of Functional Time Series in the Frequency Domain

Abstract: Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. We contribute to the research in this area by proposing stationarity tests for functional time series based on frequency domain methods. Setting up the tests requires a delicate understanding of periodogram- and spectral density operators that are the functional counterparts of periodogram- and spectral density matrices in the multivariate world. Properties of the proposed statistics are derived both under the null hypothesis of stationary functional time series and under the smooth alternative of locally stationary functional time series. The methodology is theoretically justified through asymptotic results. Evidence from simulation studies and an application to annual temperature curves suggests that the tests work well in finite samples.  

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