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Biometrika Advance Access originally published online on May 23, 2007
Biometrika 2007 94(2):347-358; doi:10.1093/biomet/asm023
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Copyright © 2007 Biometrika Trust

Articles

On the alignment of multiple time series fragments

K. Mukherjee

Department of Mathematical Sciences, The University of Liverpool, Liverpool L69 7ZL, U.K.

R. H. Shumway

Department of Statistics, University of California, Davis, California 95616, U.S.A.

K. L. Verosub

Department of Geology, University of California, Davis, California 95616, U.S.A.

k.mukherjee{at}liverpool.ac.uk

rhshumway{at}ucdavis.edu

klverosub{at}ucdavis.edu

Received for publication 1 April 2005. Accepted for publication 1 August 2006.


  Abstract

We consider a local least-squares criterion for aligning multiple time series fragments differing by locations and show the consistency of the time-lag estimator and the asymptotic normality of the location estimator. We apply the criterion to the problem of aligning 50 glacial varve fragments and construct a 3000-year surrogate for global temperature.

Key Words: Aligning time series • Asymptotics • Global warming • Lag estimator • Local least-squares • Varve chronology


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