Testing for stationarity of functional time series in the frequency domain

DOI10.1214/19-AOS1895zbMath1455.62230arXiv1701.01741MaRDI QIDQ2215748

Alexander Aue, Anne van Delft

Publication date: 14 December 2020

Published in: The Annals of Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1701.01741

zbMATH Keywords

spectral analysislocally stationary processesfunctional data analysisfrequency domain methodsannual temperature curve

Mathematics Subject Classification ID

Time series, auto-correlation, regression, etc. in statistics (GARCH) (62M10) Functional data analysis (62R10) Applications of statistics to environmental and related topics (62P12) Inference from stochastic processes and spectral analysis (62M15) Applications of statistics to physics (62P35)

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Prediction theory for stationary functional time series ⋮ White noise testing for functional time series ⋮ Nonparametric regression for locally stationary functional time series ⋮ Asymptotics for spherical functional autoregressions ⋮ Frequency domain theory for functional time series: variance decomposition and an invariance principle ⋮ A note on Herglotz's theorem for time series on function spaces ⋮ Two-Sample Tests for Relevant Differences in the Eigenfunctions of Covariance Operators ⋮ Factor models for high‐dimensional functional time series I: Representation results ⋮ INFERENCE ON THE DIMENSION OF THE NONSTATIONARY SUBSPACE IN FUNCTIONAL TIME SERIES ⋮ A portmanteau-type test for detecting serial correlation in locally stationary functional time series ⋮ Locally stationary functional time series ⋮ Graphical models for nonstationary time series ⋮ A new approach for time domain analysis of multivariate and functional time series ⋮ Functional principal component analysis for cointegrated functional time series ⋮ A similarity measure for second order properties of non-stationary functional time series with applications to clustering and testing ⋮ A nonparametric test for stationarity in functional time series ⋮ SPHARMA approximations for stationary functional time series on the sphere ⋮ Lagged covariance and cross-covariance operators of processes in Cartesian products of abstract Hilbert spaces

Uses Software

• fda (R)

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