Detection of Spatially Correlated Time Series

David Ramírez, Ignacio Santamaría and Louis Scharf
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David Ramírez: Universidad Carlos III de Madrid
Ignacio Santamaría: Universidad de Cantabria
Louis Scharf: Colorado State University

Chapter 8 in Coherence, 2022, pp 235-257 from Springer

Abstract: Abstract This chapter extends the problem of null hypothesis testing for linear independence between random variables to the problem of testing for linear independence between times series. When the time series are approximated with finite-dimensional random vectors, then this is a problem of null hypothesis testing for block-structured covariance matrices. The test statistic is a coherence statistic. It is shown to be equal in distribution to a double product of independent beta-distributed random variables. In the asymptotic case of wide-sense stationary time series, the coherence statistic may be written as a broadband coherence, with a new definition for broadband coherence. Additionally, this chapter also addresses the problem of testing for block-structured covariance, when the block structure is patterned to model cyclostationarity. Spectral formulas establish the connection with the cyclic spectrum of a cyclostationary time series.

Keywords: Spatial correlation; Broadband coherence; Cyclostationarity detection (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-031-13331-2_8

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DOI: 10.1007/978-3-031-13331-2_8

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