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Biometrika 1998 85(1):201-213; doi:10.1093/biomet/85.1.201
© 1998 by Biometrika Trust
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Matching sequences: Cross-spectral analysis of categorical time series

DAVID S. STOFFER and DAVID E. TYLER

Department of Statistics, University of Pittsburgh Pittsburgh, Pennsylvania 15260, U.S.A. stoffer{at}stat.pitt.edu
Department of Statistics, Rutgers University New Brunswick, New Jersey 08903, U.S.A. dtyler{at}stat.rutgers.edu

We consider the problem of quantifying the degree to which two stationary categorical time series are coherent. The goal is to discover whether or not the sequences contain similar patterns. The problem is motivated by the problem of matching two DNA sequences. Following the ideas used in defining the spectral envelope for a qualitativevalued time series, the methods we present here focus on the problem of obtaining coherency envelopes for measuring the similarity between two categorical time series. Estimation is based on the fast Fourier transform so that the methods are computationally simple and fast, and can be applied to long sequences.

Key Words: Canonical analysis • Coherency • DNA sequences • Numerical maximisation


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