Estimation of a Common Group Delay Between Two Multiple Time Series

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Abstract
The group delay at frequency λ between two univariate time series represents the time lag of the harmonic component at frequency λ of the first series behind the corresponding harmonic component of the second series. This article proposes an estimate of group delay under conditions that arise in dendrochronology where each of A tree ring time series shares a common group delay with each of B other tree ring time series and where the common group delay is constant over a frequency band. The asymptotic properties of the estimation procedure are investigated, and the application of the procedure to dendrochronology is emphasized and illustrated.

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