A nonparametric test for stationarity in functional time series

  title={A nonparametric test for stationarity in functional time series},
  author={Anne van Delft and Vaidotas Characiejus and Holger Dette},
We propose a new measure for stationarity of a functional time series, which is based on an explicit representation of the $L^2$-distance between the spectral density operator of a non-stationary process and its best ($L^2$-)approximation by a spectral density operator corresponding to a stationary process. This distance can easily be estimated by sums of Hilbert-Schmidt inner products of periodogram operators (evaluated at different frequencies), and asymptotic normality of an appropriately… 

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