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Detection of Spatially Correlated Time Series

In: Coherence

Author

Listed:
  • David Ramírez

    (Universidad Carlos III de Madrid)

  • Ignacio Santamaría

    (Universidad de Cantabria)

  • Louis Scharf

    (Colorado State University)

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.

Suggested Citation

  • David Ramírez & Ignacio Santamaría & Louis Scharf, 2022. "Detection of Spatially Correlated Time Series," Springer Books, in: Coherence, chapter 8, pages 235-257, Springer.
    • Handle: RePEc:spr:sprchp:978-3-031-13331-2_8
    DOI: 10.1007/978-3-031-13331-2_8
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