van Delft, AnneDette, Holger2018-12-042018-12-042018http://hdl.handle.net/2003/3782810.17877/DE290R-19823Due to the surge of data storage techniques, the need for the development of appropri-ate techniques to identify patterns and to extract knowledge from the resulting enormous data sets, which can be viewed as collections of dependent functional data, is of increasing interest in many scientific areas. We develop a similarity measure for spectral density oper-ators of a collection of functional time series, which is based on the aggregation of Hilbert-Schmidt differences of the individual time-varying spectral density operators. Under fairly general conditions, the asymptotic properties of the corresponding estimator are derived and asymptotic normality is established. The introduced statistic lends itself naturally to quantify (dis)-similarity between functional time series, which we subsequently exploit in order to build a spectral clustering algorithm. Our algorithm is the first of its kind in the analysis of non-stationary (functional) time series and enables to discover particular pat-terns by grouping together ‘similar’ series into clusters, thereby reducing the complexity of the analysis considerably. The algorithm is simple to implement and computationally fea-sible. As a further application we provide a simple test for the hypothesis that the second order properties of two non-stationary functional time series coincide.enDiscussion Paper / SFB823;33/2018time serieslocal stationarityspectral analysisclusteringfunctional data310330620working paper