A0161
Title: Testing stationarity of functional time series in the frequency domain
Authors: Alexander Aue - UC Davis (United States) [presenting]
Anne van Delft - Columbia University (United States)
Abstract: Interest in functional time series has spiked in the recent past with both methodology and applications. A new stationarity test is discussed for functional time series based on frequency-domain methods. The proposed test statistic is based on joint dimension reduction via functional principal components analysis across the spectral density operators at all Fourier frequencies, explicitly allowing for frequency-dependent levels of truncation to adapt to the dynamics of the underlying functional time series. The properties of the test 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 test works well in finite samples.
