van Delft, Anne2019-09-062019-09-062019http://hdl.handle.net/2003/3820510.17877/DE290R-20184We study the distributional properties of a quadratic form of a stationary functional time series under mild moment conditions. As an important application, we obtain consistency rates of estimators of spectral density operators and prove joint weak convergence to a vector of complex Gaussian random operators. Weak convergence is established based on an approximation of the form via transforms of Hilbert-valued martingale difference sequences. As a side-result, the distributional properties of the long-run covariance operator are established.enDiscussion Paper / SFB823;18/2019functional datamartingalesspectral analysistime series310330620working paper