A note on quadratic forms of stationary functional time series under mild conditions

Anne van Delft

Stochastic Processes and their Applications, 2020, vol. 130, issue 7, 4206-4251

Abstract: We study 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.

Keywords: Functional data; Time series; Spectral analysis; Martingales (search for similar items in EconPapers)
Date: 2020
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Citations: View citations in EconPapers (1)

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DOI: 10.1016/j.spa.2019.12.002

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