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Biometrika 1971 58(3):469-481; doi:10.1093/biomet/58.3.469
© 1971 by Biometrika Trust
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The estimation of coherence and group delay

E. J. HANNAN and P. J. THOMSON

The Australian National University

The usual estimation of coherence is known to be badly biased towards zero if over the band of frequencies used for its estimation the phase is changing rapidly, as in the case of large group delay. The usual asymptotic distribution theory for spectral estimates is of no value in this circumstance, since it does not involve the group delay. A new theory is used to obtain estimates of coherence and group delay, which is itself of considerable physical interest, and the asymptotic distribution of the estimates is obtained.

Key Words: Multiple time series • Coherency • Group delay • Cross-spectral analysis


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