Nonparametric Spectral Analysis of Multivariate Time Series

Spectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years. Since the success of the fast Fourier transform algorithm, the analysis of serial auto- and cross-correlation in the frequency domain has helped us to understand the...

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Bibliographic Details
Published in:Annual review of statistics and its application 2020-03, Vol.7 (1), p.361-386
Main Author: von Sachs, Rainer
Format: Article
Language:English
Subjects:
coherency
Fourier
locally stationary time series
positive-definiteness
smoothing
wavelets
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Summary:Spectral analysis of multivariate time series has been an active field of methodological and applied statistics for the past 50 years. Since the success of the fast Fourier transform algorithm, the analysis of serial auto- and cross-correlation in the frequency domain has helped us to understand the dynamics in many serially correlated data without necessarily needing to develop complex parametric models. In this work, we give a nonexhaustive review of the mostly recent nonparametric methods of spectral analysis of multivariate time series, with an emphasis on model-based approaches. We try to give insights into a variety of complimentary approaches for standard and less standard situations (such as nonstationary, replicated, or high-dimensional time series), discuss estimation aspects (such as smoothing over frequency), and include some examples stemming from life science applications (such as brain data).
ISSN:2326-8298
2326-831X
DOI:10.1146/annurev-statistics-031219-041138